Wheel lifted and grounded identification for an automotive vehicle

ABSTRACT

A control system ( 18 ) for an automotive vehicle ( 10 ) has a first roll condition detector ( 64 A), a second roll condition detector ( 64 B), a third roll condition detector ( 64 C), and a controller ( 26 ) that uses the roll condition generated by the roll condition detectors ( 64 A-C) to determine a wheel lift condition. Other roll condition detectors may also be used in the wheel lift determination. The wheel lift conditions may be active or passive or both.

RELATED APPLICATIONS

The present invention is a continuation application of U.S. patentapplication No. 10/608,909, filed on Jun. 27, 2003, now U.S Pat. No.7,109,856 entitled “Wheel Lift Identification for an AutomotiveVehicle”, which claims priority to U.S. provisional patent applicationSer. Nos. 60/400,375, 60/400,261, 60/400,172, 60/400,376, 60/400,156,and 60/400,155, all filed on Aug. 1, 2002, and 60/401,418 filed on Aug.5, 2002. U.S. patent application Ser. No. 10/808,909 is acontinuation-in-part of U.S. patent application Ser. No. 10/038,364filed on Jan. 4, 2002 now U.S. Pat. No. 6,593,849 entitled “Wheel LiftIdentification For An Automotive Vehicle”, which is acontinuation-in-part of U.S. patent application Ser. No. 09/669,513filed on Sep. 25, 2000 now U.S. Pat. No. 6,356,188 entitled “Wheel LiftIdentification For An Automotive Vehicle”, each of which are herebyincorporated by reference herein, as well as U.S. patent applicationSer. No. 10/608,908 filed on Jun. 27, 2003; U.S. patent application Ser.No. 10/609,448 filed on Jun. 27, 2003 now U.S. Pat. No. 7,132,937 issuedon Nov. 7, 2006; and U.S. patent application Ser. No. 10/609,447 filedon Jun. 27, 2003 now U.S. Pat. No. 6,904,350 issued on Jun. 7, 2005,filed simultaneously with U.S. patent application Ser. No. 10/608,909.

TECHNICAL FIELD

The present embodiment relates generally to a control apparatus forcontrolling a system of an automotive vehicle in response to senseddynamic behavior, and more specifically, to a method and apparatus fordetermining whether a wheel of an automotive vehicle has lifted from thepavement using passive wheel lift detection.

BACKGROUND

Dynamic control systems for automotive vehicles have recently begun tobe offered on various products. Dynamic control systems typicallycontrol the yaw of the vehicle by controlling the braking effort at thevarious wheels of the vehicle. Yaw control systems typically compare thedesired direction of the vehicle based upon the steering wheel angle andthe direction of travel. By regulating the amount of braking at eachcorner of the vehicle, the desired direction of travel may bemaintained. Typically, the dynamic control systems do not addressrollover (wheels lifting) of the vehicle. For high profile vehicles inparticular, it would be desirable to control the rollover characteristicof the vehicle to maintain the vehicle position with respect to theroad. That is, it is desirable to maintain contact of each of the fourtires of the vehicle on the road.

In vehicle rollover control, it is desired to alter the vehicle attitudesuch that its motion along the roll direction is prevented fromachieving a predetermined limit (rollover limit) with the aid of theactuation from the available active systems such as controllable brakesystem, steering system and suspension system. Although the vehicleattitude is well defined, direct measurement is usually impossible.

During a potential vehicular rollover event, wheels on one side of thevehicle start lifting, and the roll center of the vehicle shifts to thecontact patch of the remaining tires. This shifted roll center increasesthe roll moment of inertia of the vehicle, and hence reduces the rollacceleration of the vehicle. However, the roll attitude could stillincrease rapidly. The corresponding roll motion when the vehicle startsside lifting deviates from the roll motion during normal drivingconditions.

When the wheels start to lift from the pavement, it is desirable toconfirm this condition. This allows the system to make an accuratedetermination as to the appropriate correction. If wheels are on theground, or recontact the ground after a lift condition, this alsoassists with accurate control.

Some systems use position sensors to measure the relative distancebetween the vehicle body and the vehicle suspension. One drawback tosuch systems is that the distance from the body to the road must beinferred. This also increases the number of sensors on the vehicle.Other techniques use sensor signals to indirectly detect wheel liftingqualitatively.

One example of a wheel lifting determination can be found in U.S. Pat.No. 6,356,188. The system applies a change in torque to the wheels todetermine wheel lift. The output from such a wheel lifting determinationunit can be used qualitatively. This method is an active determinationsince the basis of the system relies on changing the torque of thewheels by the application of brakes or the like. In some situations itmay be desirable to determine wheel lift without changing the torque ofa wheel.

It would therefore be desirable to provide a rollover detection systemthat improves reliability in predicting the occurrence of wheel liftduring the operation of the automotive vehicle.

SUMMARY

It is therefore one object of the invention to provide a rolloverdetection system that may be used in conjunction with the dynamicstability control system of the vehicle to determine the presence of apotential rollover. The present invention seeks to determine the rollcondition and wheel lifting in a number of ways using the sensorsavailable from the vehicle control system. The various roll conditionsare compared to roll thresholds to determine the likelihood that thewheel has lifted. The control system then can make a determination as tohow to command the appropriate actuators to correct the potentialrollover condition.

In one aspect of the invention, a wheel lift identification system foran automotive vehicle includes a first roll condition detector, a secondroll condition detector, and a third roll condition detector. Acontroller determines wheel lift in response to the first, second, andthird roll conditions.

In a further aspect of the invention, a method of controlling a vehiclehaving a plurality of wheels comprises determining a relative rollangle, determining a wheel departure angle, determining a rollingradius-based wheel departure angle, determining normal loading at eachwheel, determining an actual road torque, determining a wheellongitudinal slip; and determining a wheel lift status for saidplurality of wheels in response to said relative roll angle, said wheeldeparture angle, said rolling radius-based wheel departure roll angle,the normal loading at each wheel, an actual road torque and the wheellongitudinal slip.

One advantage of the invention is that by providing such a system animproved determination of wheel lifting may be determined. The accuracyof the roll angle calculation may correspondingly be increased,resulting in a more appropriate braking or steering evasive action.

Other advantages and features of the present invention will becomeapparent when viewed in light of the detailed description when taken inconjunction with the attached drawings and appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic view of a vehicle with variable vectors andcoordinate frames according to one embodiment of the present invention.

FIG. 2A is a block diagram of a stability system according to oneembodiment of the present invention.

FIG. 2B is a block diagrammatic view of the wheel lift detection systemof FIG. 2A.

FIG. 2C is a block diagrammatic view of the rollover stability controlfeedback command of FIG. 2A.

FIG. 3 is a diagrammatic view of a vehicle showing the displacement ofthe vehicle body and axle relative to road surface.

FIG. 4 is a diagrammatic view showing the forces applied to the frontwheel/tire/suspension assembly during a potential rollover event.

FIG. 5 is a diagrammatic view showing the forces applied to the rearwheel/tire/suspension assembly during a potential rollover event.

FIG. 6 is flow chart of a passive wheel lift determination according toone embodiment of the present invention.

FIG. 7 is a flow chart of an active wheel lift identification systemaccording to one embodiment of the present invention.

FIG. 8A is a plot of pressure versus time for a wheel liftidentification system according to one embodiment of the presentinvention.

FIG. 8B is a plot of wheel speed versus time for a wheel liftidentification system according to one embodiment of the presentinvention.

FIG. 9 is a flow chart illustrating a plot of a passive wheel liftdetection using the operating torque of the vehicle.

FIG. 10 is an end view of an automotive vehicle on a bank.

FIG. 11 is a block diagrammatic view of the controller.

FIG. 12 is a high level flow chart illustrating condition detection andthe resulting actions.

FIG. 13 is a flow chart of a drive train based decision step 302 of FIG.12.

FIG. 14 is a flow chart of the passive wheel lift grounding detectionstep 304 of FIG. 12.

FIG. 15 is a flow chart of the active wheel lift grounding detectionstep 308 of FIG. 12.

FIG. 16 is a flow chart of the resulting actions step 312 of FIG. 12.

DETAILED DESCRIPTION

In the following figures the same reference numerals will be used toidentify the same components. The present invention may used inconjunction with a rollover control system for a vehicle. However, thepresent embodiment may also be used with a deployment device such asairbag or roll bar. The present invention will be discussed below interms of embodiments relating to an automotive vehicle moving in athree-dimensional road terrain.

Wheel lift detection is the determination of when a wheel has liftedfrom the pavement. A passive system determines wheel lift indirectlyusing outputs from various sensors without perturbing the vehicle orwheels.

One aspect of the invention is passive wheel detection which is named incomparison with the so-called active wheel lift detection of U.S. Pat.No. 6,356,188. In active wheel lift detection, the wheel lifting isidentified by requesting a change in torque at a wheel such as byapplying a small amount of pressure in each wheel and then checking whatthe wheel slip ratio is doing. In passive wheel lift detection as setforth herein, the available sensor signals are used to identify wheellifting without the system requiring a pressure command to the brakesystem of each wheel. Of course, as will be described below, active andpassive detection may be used together. Wheel lifting typically occurson the wheels on the inside of a turn. Depending on the vehicleconfiguration such as suspension, the front wheel or rear wheel may liftfirst.

Another aspect includes active and passive and yet another includes rollangle correction in response to wheel lift grounding.

Referring to FIG. 1, an automotive vehicle 10 with a safety system ofthe present invention is illustrated with the various forces and momentsthereon during a rollover condition. Vehicle 10 has front right (FR) andfront left (FL) wheel/tires 12A and 12B and rear right (RR) wheel/tires13A and rear left (RL) tires 13B respectively. These tires areparenthetically identified 0, 1, 2, and 3 in some embodiments below. Thevehicle 10 may also have a number of different types of front steeringsystems 14 a and rear steering systems 14 b including having each of thefront and rear wheels configured with a respective controllableactuator, the front and rear wheels having a conventional type system inwhich both of the front wheels are controlled together and both of therear wheels are controlled together, a system having conventional frontsteering and independently controllable rear steering for each of thewheels or vice versa. Generally, the vehicle has a weight represented asMg at the center of gravity of the vehicle, where g=9.8 m/s² and M isthe total mass of the vehicle.

As mentioned above, the system may also be used with safety systemsincluding active/semi-active suspension systems, anti-roll bar, orairbags or other safety devices deployed or activated upon sensingpredetermined dynamic conditions of the vehicle.

The sensing system 16 is coupled to a control system 18. The sensingsystem 16 may comprise many different sensors including the sensor settypically found in a yaw control system (including lateralaccelerometer, yaw rate sensor, steering angle sensor and wheel speedsensors) together with a roll rate sensor, a vertical accelerometer, anda longitudinal accelerometer. The various sensors will be furtherdescribed below. The present embodiment uses the various sensors todetermine wheel lift. The sensors may also be used by the control systemin various determinations such as to determine a lifting event. Thewheel speed sensors 20 are mounted at each corner of the vehicle andgenerate signals corresponding to the rotational speed of each wheel.The rest of the sensors of sensing system 16 may be mounted directly onthe center of gravity of the vehicle body, along the directions x,y andz shown in FIG. 1. As those skilled in the art will recognize, the framefrom b₁, b₂ and b₃ is called a body frame 22, whose origin is located atthe center of gravity of the car body, with the b₁ corresponding to thex axis pointing forward, b₂ corresponding to the y axis pointing off thedriving side (to the left), and the b₃ corresponding to the z axispointing upward. The angular rates of the car body are denoted abouttheir respective axes as w_(x) for the roll rate, w_(y) for the pitchrate and w_(z) for the yaw rate. The calculations may take place in aninertial frame 24 that may be derived from the body frame 22 asdescribed below.

The angular rate sensors and the accelerometers may be mounted on thevehicle car body along the body frame directions b₁ and b₃, which arethe x-y-z axes of the sprung mass of the vehicle.

The longitudinal acceleration sensor is mounted on the car body locatedat the center of gravity, with its sensing direction along b₁-axis,whose output is denoted as a_(x). The lateral acceleration sensor ismounted on the car body and may be located at the center of gravity,with its sensing direction along b₂-axis, whose output is denoted asa_(y).

The other frame used in the following discussion includes the roadframe, as depicted in FIG. 1. The road frame system r₁r₂r₃ is fixed onthe driven road surface, where the r₃ axis is along the average roadnormal direction computed from the normal directions of thefour-tire/road contact patches.

In the following discussion, the Euler angles of the body frame b₁b₂b₃with respect to the road frame r₁r₂r₃ are denoted as θ_(xbr), θ_(ybr)and θ_(zbr), which are also called the relative Euler angles (i.e.,relative roll, relative pitch and relative yaw angles, respectively).

Referring now to FIG. 2, roll stability control system 18 is illustratedin further detail having a controller 26 used for receiving informationfrom a number of sensors which may include a yaw rate sensor 28, a speedsensor 20, a lateral acceleration sensor 32, a vertical accelerationsensor 33, a roll angular rate sensor 34, a steering wheel (hand wheel)angle sensor 35, a longitudinal acceleration sensor 36, a pitch ratesensor 37, steering angle (of the wheels or actuator) position sensor38, suspension load sensor 40 and suspension position sensor 42.

Controller 26 may include a signal multiplexer 50 that is used toreceive the signals from the sensors 28-42. The signal multiplexer 50provides the signals to a wheel lift detector 52, a vehicle roll anglecalculator 54, and to a roll stability control (RSC) feedback controlcommand 56. Also, wheel lift detector 52 may be coupled to the vehicleroll angle calculator 54. The vehicle roll angle calculator 54 may alsobe coupled to the RSC feedback command 56. Vehicle roll angle calculator54 is described in provisional applications 60/400,376 and 60/400,172,and U.S. application (Docket No. 201-0938/FGT 1660), the disclosures ofwhich are incorporated herein by reference.

Referring now also to FIG. 2B, the wheel lift detector 52 may includepassive wheel detector 58 as will be further described herein, activewheel detector 60 as described above with respect to the prior art andan integrated wheel lift detector 62. Thus, both active and passive maybe used together. As will be further described below, an arbitrationscheme between the active and passive lifting may be used in a wheelfinal lift determination within the integrated wheel lift detector 62.

Referring now also to FIG. 2C, the roll stability control (RSC)controller 26 may also include a first roll condition detector 64A, asecond roll condition detector 64B, a third roll condition detector 64C,a fourth roll condition detector 64D, and a roll event sensor 66. Itshould be noted that the implementation of the wheel lift detector 52,the vehicle roll angle calculator 54, the roll stability controlfeedback control command 56 having a torque control system 57 (describedfurther below), the passive wheel lift detection 58, the active wheellift detection 60, and the integrated wheel lift detection 62 may all beincorporated in software within the controller 26. Separate controldevices may also be used.

Wheel lift detector 52 determines a qualitative determination of vehiclerollover. This is in contrast to the vehicle roll angle calculator 54,which is a quantitative determination of rollover. Active wheel liftdetector 60 can be determined in many ways including U.S. ProvisionalApplications 60/400,375 and 60/400,156, both filed Aug. 1, 2002, andU.S. Pat. No. 6,356,188, the disclosures of which are incorporated byreference herein. The integrated wheel lift detector 62 is set forth inU.S. Provisional Application 60/401,418 filed Aug. 5, 2002, thedisclosure of which is incorporated herein. Vehicle roll anglecalculator 54 is described in U.S. Provisional Applications 60/400,376and 60/400,172, both filed Aug. 1, 2002, and Ford Disclosure 201-0938(FGT 1660), which are incorporated by reference herein.

In one embodiment the sensors are located at the center of gravity ofthe vehicle. Those skilled in the art will recognize that the sensor mayalso be located off the center of gravity and translated equivalentlythereto.

Lateral acceleration, roll orientation and speed may be obtained using aglobal positioning system (GPS). Based upon inputs from the sensors,controller 26 may control a safety device 44. Depending on the desiredsensitivity of the system and various other factors, not all the sensors28-42 may be used in a commercial embodiment. Safety device 44 maycontrol an airbag 45 or a steering actuator/braking actuator 46A-D atone or more of the wheels 12A, 12B, 13A, 13B of the vehicle. Also, othervehicle components such as a suspension control 48 may be used to adjustthe suspension to prevent rollover.

Roll angular rate sensor 34 and pitch rate sensor 37 may sense the rollcondition or lifting of the vehicle based on sensing the height of oneor more points on the vehicle relative to the road surface. Sensors thatmay be used to achieve this include a radar-based proximity sensor, alaser-based proximity sensor and a sonar-based proximity sensor.

Roll rate sensor 34 and pitch rate sensor 37 may also sense the rollcondition or lifting based on sensing the linear or rotational relativedisplacement or displacement velocity of one or more of the suspensionchassis components. This may be in addition to or in combination withsuspension position sensor 42. The position sensor 42, roll rate sensor34 and/or the pitch rate sensor 37 may include a linear height or travelsensor, a rotary height or travel sensor, a wheel speed sensor used tolook for a change in velocity, a steering wheel position sensor, asteering wheel velocity sensor and a driver heading command input froman electronic component that may include steer by wire using a handwheel or joy stick.

The roll condition or lifting may also be sensed by sensing directly orestimating the force or torque associated with the loading condition ofone or more suspension or chassis components including a pressuretransducer in an air suspension, a shock absorber sensor such as a loadsensor 40, a strain gauge, the steering system absolute or relativemotor load, the steering system pressure of the hydraulic lines, a tirelateral force sensor or sensors, a longitudinal tire force sensor, avertical tire force sensor or a tire sidewall torsion sensor. The yawrate sensor 28, the roll rate sensor 34, the lateral acceleration sensor32, and the longitudinal acceleration sensor 36 may be used together todetermine that the wheel has lifted. Such sensors may be used todetermine wheel lift or estimate normal loading associated with wheellift. These are passive methods as well.

The roll condition of the vehicle may also be established by one or moreof the following translational or rotational positions, velocities oraccelerations of the vehicle including a roll gyro, the roll rate sensor34, the yaw rate sensor 28, the lateral acceleration sensor 32, thevertical acceleration sensor 33, a vehicle longitudinal accelerationsensor 36, lateral or vertical speed sensor including a wheel-basedspeed sensor 20, a radar-based speed sensor, a sonar-based speed sensor,a laser-based speed sensor or an optical-based speed sensor.

Safety device 44 may control the position of the front right wheelactuator 46A, the front left wheel actuator 46B, the rear left wheelactuator 46C, and the right rear wheel actuator 46D. Although asdescribed above, two or more of the actuators may be simultaneouslycontrolled. For example, in a rack-and-pinion system, the two wheelscoupled thereto are simultaneously controlled. Based on the inputs fromsensors 28 through 42, controller 26 determines a roll condition and/orwheel lift and controls the steering position of the wheels.

Speed sensor 20 may be one of a variety of speed sensors known to thoseskilled in the art. For example, a suitable speed sensor may include asensor at every wheel that is averaged by controller 26. The controllermay translate the wheel speeds into the speed of the vehicle. Yaw rate,steering angle, wheel speed and possibly a slip angle estimate at eachwheel may be translated back to the speed of the vehicle at the centerof gravity. Various other algorithms are known to those skilled in theart. Speed may also be obtained from a transmission sensor. For example,if speed is determined while speeding up or braking around a corner, thelowest or highest wheel speed may not be used because of its error.Also, a transmission sensor may be used to determine vehicle speed.

Load sensor 40 may be a load cell coupled to one or more suspensioncomponents. By measuring the stress, strain or weight on the load sensora shifting of the load can be determined.

Several different combinations of sensors may be used to determine awheel lift status. Once the qualitative wheel lift is determined,quantitative roll condition may be determined. The following is asummary of how the quantitative wheel lifting indication from thevarious vehicle motion variables after qualitative wheel lifting statusis identified.

The roll condition of a vehicle can be characterized by the relativeroll angle between the vehicle body and the wheel axle and the wheeldeparture angle (between the wheel axle and the average road surface).Both the relative roll angle and the wheel departure angle may becalculated in relative roll angle estimation module by using the rollrate and lateral acceleration sensor signals. If both the relative rollangle and the wheel departure angles are large enough, the vehicle maybe in either single wheel lifting or double wheel lifting. On the otherhand, if the magnitude of both angles are small enough, the wheels arelikely all grounded.

The roll condition of a vehicle can be characterized by rollingradius-based wheel departure roll angle, which captures the anglebetween the wheel axle and the average road surface through the dynamicrolling radii of the left and right wheels when both of the wheels aregrounded. Since the computation of the rolling radius is related to thewheel speed and the linear velocity of the wheel, such rolling-radiusbased wheel departure angle will assume abnormal values when there arelarge wheel slips. This happens when a wheel is lifted and there istorque applied to the wheel. Therefore, if this rolling radius-basedwheel departure angle is increasing rapidly, the vehicle might havelifted wheels. Small magnitude of this angle indicates the wheels areall grounded.

The roll condition of the vehicle can be seen indirectly from the wheellongitudinal slip. If during a normal braking or driving torque thewheels at one side of the vehicle experience increased magnitude ofslip, then the wheels of that side are losing longitudinal road torque.This implies that the wheels are either driven on a low mu surface orlifted up.

The roll condition of the vehicle can be characterized by the normalloading sustained at each wheel. Theoretically, when a normal loading ata wheel decreases to zero, the wheel is no longer contacting the roadsurface. In this case a potential rollover is under the way. Largemagnitude of this loading indicates that the wheel is grounded.

The roll condition can be identified by checking the actual road torquesapplied to the wheels and the road torques, which are needed to sustainthe wheels when they are grounded. The actual road torques can beobtained through torque balancing for each wheel using wheelacceleration, driving torque and braking torque. If the wheel iscontacting the road surface, the calculated actual road torques mustmatch or be larger than the nonlinear torques calculated from the normalloading and the longitudinal slip at each wheel.

Relative Roll Angle and Wheel Departure Angle Using Lateral Accelerationand Roll Angular Rate Sensor

The roll condition of a vehicle can be characterized by the relativeroll angle θ_(xr) between the vehicle body and the wheel axle, which hasbeen calculated by using the roll rate and lateral acceleration sensorsignals. If this roll angle is increasing rapidly, the vehicle might bein the edge of wheel lifting or rollover. Small magnitude of this angleindicates the wheels are not lifted or are all grounded.

The roll condition of a vehicle can also be characterized by the rollangle between the wheel axle and the average road surface, this iscalled wheel departure angle. If this roll angle is increasing rapidly,the vehicle has lifted wheel or wheels and aggressive control actionneeds to be taken in order to prevent the vehicle from rolling over.Small magnitude of this angle indicates the wheels are not lifted. Thissection describes how to quantitatively determine the vehicle roll anglewhen a qualitative wheel lifting is identified. That is, if aqualitative wheel lifting is detected, a quantitative computation of thewheel lifting may be initiated.

Referring now to FIGS. 3, 4 and 5, the present invention will bediscussed below in terms of embodiments relating to an automotivevehicle having a wheel/tire/suspension assembly 354 during potentialrollover events where one side of the vehicle is lifted or wheels on oneside of the vehicle lose contact with the road surface or wheels on oneside do not carry normal loadings. The wheel/tire/suspension assemblyhas an axle 356. Although a physical axle may not be present, axle is aterm used for the common axis of the front or rear wheels.

The sensing system uses the lateral acceleration sensor 32 and the rollangular rate sensor 34 to determine wheel lift in one of the rollcondition detectors 64A-D. The lateral acceleration sensor 32 is used tomeasure the total lateral acceleration of the center of gravity of thevehicle body, and the roll rate sensor 34 measures the vehicle body rollangular rate. The method of determining wheel lifting using the rollrate sensor 34 and the lateral acceleration sensor 32 is described inU.S. Patent Application (Docket Number 201-0938/FGT 1660), thedisclosure of which is incorporated by reference.

The vehicle body 10 is connected with the wheel/tire assemblies 12A,12B, 13A, 13B through suspensions 360 _(lr), 360 _(rr), 360 _(lf), and360 _(rf), collectively suspension 360. The tire forces are transferredto the vehicle body through the suspensions 360. Those forces can beprojected along the vehicle body-fixed y- and z-axes. The suspensionforces projected along the body-fixed y axis (or body-fixed lateraldirection) are denoted as S_(ylf), S_(yrf), S_(ylr), S_(yrr) at theleft-front, right-front, left-rear and right-rear corners; thesuspension forces projected along the body-fixed z axis (or body-fixedvertical direction) as S_(zlf), S_(zrf), S_(zlr), S_(zrr). The totallateral forces applied to the vehicle body along the body-fixed lateralaxis are S_(y), i.e.S _(y) =S _(ylf) +S _(yrf) +S _(ylr) +S _(yrr).  (1)

The vehicle body has roll angular displacement due to the suspensionforces and the vehicle roll accelerations. The roll angular rate of thevehicle body is w_(x). Around center of gravity of the vehicle body, thesuspension forces-induced roll moment around the vehicle center ofgravity (c.g.) needs to match the inertia moment from this w_(x). Thesuspension forces-induced roll moment around the c.g. has two terms:

the roll moment M_(susp-vert) due to the vertical suspension forcesS_(zlf), S_(zrf), S_(zlr), S_(zrr);

the roll moment M_(susp-lat)due to the total lateral suspension forceS_(y).

From FIG. 5, the following expressions for M_(susp-vert) andM_(susp-lat) may be obtainedM _(susp-vert)=(S _(zrf) −S _(zlf) +S _(zrr) −S _(zlr))lM _(susp-lat) =S _(y) h _(cg).  (2)

The vehicle body roll angular rate must satisfy the followingI _(x) {dot over (w)} _(x) =M _(susp-vert) +M _(susp-lat)  (3)where I_(x) is the vehicle body roll moment of inertia around the c.g.of the vehicle body. If the suspension resultant roll stiffness and rolldamping rates (including anti-roll-bars, suspensions, etc.) arerespectively defined as K_(roll) and D_(roll), and θ_(bw) as therelative angular displacement between the vehicle body and the averagewheel axle, then the roll moment due to vertical suspension forcesM_(susp-vert) can be further expressed asM _(susp-vert) =−K _(roll)θ_(bw) −D _(roll){dot over (θ)}_(bw).  (4)

The roll moment due to lateral suspension forces M_(susp-lat) needs tobe further defined so that the roll angular rate sensors and the lateralaccelerometer may be used. The longitudinal and lateral velocities ofthe c.g. of the vehicle body are v_(x) and v_(y), which are measuredalong body-fixed x- and y-axis respectively, and w_(z) is the yaw rateof the vehicle. The lateral dynamics of the vehicle body will satisfythe following equation of motion based on Newton's law:M _(s)({dot over (v)} _(y) +w _(z) v _(x))=S _(y) +M _(s) gsin(θ_(bw)+θ_(wr))  (5)where θ_(wr) is the relative angular displacement between the wheel axleand the road surface, (or the departure angle of the wheel axle from theroad surface), M_(s) is the vehicle body mass (or the sprung mass of thevehicle). Solving S_(y) from (5) and substituting S_(y) into the secondequation of (2) leads toM _(susp-lat) =M _(s)({dot over (v)} _(y) +w _(z) v _(x))h _(cg) −M _(s)g sin(θ_(bw)+θ_(wr))h _(cg).  (6)

The dynamic equation to depict the wheel axle departure angle from theroad surface. There are two wheel sets, one on the front (FIG. 4) andone on the rear (FIG. 5). Due to the differences in front and rearsuspensions and inertias, there are slight differences between the frontand the rear wheel axle departure angles. θ_(wr-front) is denoted as thefront wheel departure angle and θ_(wr-rear) is denoted as the rear wheeldeparture angle. The average of those two angles is used to define theangle θ_(wr)

$\begin{matrix}{\theta_{wr} = {\frac{\theta_{{wr} - {front}} + \theta_{{wr} - {rear}}}{2}.}} & (7)\end{matrix}$

The assembly consists of the wheel, the tires and the suspensions. FIG.5 shows the rear axle of such assembly. In order to avoid solving thefront lateral and vertical tire forces F_(yf) and F_(zf), the rearlateral and vertical tire forces F_(yr) and F_(zr), the equation ofmotion was written around the outer tire contact patch for front andrear assembliesI _(wxf){umlaut over (θ)}_(wr)=(h−h _(cg))cos(θ_(bw))[S _(ylf) +S _(yrf)]−M _(uf) gl _(w) cos(θ_(wr))+(S _(zlf) −S _(zrf))lI _(wxr){umlaut over (θ)}_(wr)=(h−h _(cg))cos(θ_(bw))[S _(ylr) +S _(yrr)]−M _(ur) gl _(w) cos(θ_(wr))+(S _(zlr) −S _(zrr))l  (8)where h_(cg) is the distance between the vehicle body c.g. and the roadsurface when the car is parked; I_(wxf) and I_(wxr) are the roll momentsof inertia of the front and rear wheel/tire/suspension assemblies aroundthe contact patches of the outer tires; M_(uf) and M_(ur) are the totalmasses of the front and rear wheel/tire/suspension assemblies; l_(w) isthe half of the wheel track.

Up to now, vehicle states or motion variables were associated with therelative roll angles of interest. The goal is to determine the relativeroll angles with the available sensor signals. In order to establish theconnection, the sensor signals are related with those motion variablesused to derive equations (3) and (8). First consider the lateralacceleration sensor output, which is denoted as a_(y-sensor). Themeasured signal a_(y-sensor) includes various components due to thevehicle yaw, longitudinal, lateral motions and gravity, and it can berelated to the lateral, longitudinal, yaw motion variables and thegravity, as in the following:a _(y-sensor) ={dot over (v)} _(y) +w _(z) v _(x) −gsin(θ_(bw)+θ_(wr))  (9)and the roll angular rate sensor output measures the same roll rate usedbefore, i.e.,w_(x-sensor)=w_(x).  (10)

Substituting (9) into (5) leads toM_(susp-lat)=M_(s)h_(cg)a_(y-sensor)S_(y)=M_(s)a_(y-sensor).  (11)

Therefore (3) can be simplified into{dot over (θ)}_(bw) =−c ₁θ_(bw) −c ₂ {dot over (w)} _(x-sensor) +c ₃ a_(y-sensor)  (12)where the coefficients in the equation can be related to the vehicleparameters as in the following:

${c_{1} = {- \frac{K_{roll}}{D_{roll}}}},\mspace{14mu}{c_{2} = \frac{I_{x}}{D_{roll}}},\mspace{14mu}{c_{3} = {\frac{M_{s}h_{cg}}{D_{roll}}.}}$

Adding together the two equations in (8) and Substituting (11) into theresultant equation leads to the following equation{umlaut over (θ)}_(wr) =−d ₁ cos(θ_(wr))+d ₂ a _(y-sensor) cos(θ_(bw))+d₃θ_(bw) +d ₄{dot over (θ)}_(bw)  (13)where the coefficients in the equation can be related to the vehicleparameters as

$\begin{matrix}{{d_{1} = {\frac{\left( {M_{uf} + M_{ur}} \right)l_{w}}{I_{wxf} + I_{wxr}}g}},} & {{d_{2} = \frac{M_{s}\left( {h - h_{cg}} \right)}{I_{wxf} + I_{wxr}}},} \\{{d_{3} = \frac{K_{roll}}{I_{wxf} + I_{wxr}}},} & {d_{4} = {\frac{D_{roll}}{I_{wxf} + I_{wxr}}.}}\end{matrix}$

Based on (12) and, the angles of interests can be related to the twosensor signals a_(y-sensor) and w_(x-sensor). A digital algorithm usinga Tyler expansion to the continuous time differential equation in orderto obtain the digital version of the sensing algorithm can be used as inthe following for estimating the relative roll anglesθ_(bw)(k+1)=θ_(bw)(k)+ΔT*f(k)x(k+1)=x(k)+ΔT*g(k)θ_(wr)(k+1)=θ_(wr)(k)+ΔT*x(k)+ΔT² *g(k)  (14)where ΔT is the sampling time of the implemented algorithm,f(k)=−c ₁θ_(bw)(k)−c ₂ w _(x-sensor)(k)+c ₃ a _(y-sensor)(k)g(k)=−d ₁ cos(θ_(wr)(k))+d ₂ a _(y-sensor)(k)cos(θ_(bw)(k))+d₃θ_(bw)(k)+d ₄θ_(bw)(k).  (15)

In a digital implementation, the previously known angles are iterativelyused in the angle determinations. This reduces the over all number ofprocessing steps which leads to faster results and ultimately thoseangles add more control authority to the potential vehicle rolloverevent.

Since the quantitative determination of the wheel departure angle as in(14) depends on when the computation should be started, a qualitativerollover indication is required. One of such qualitative rolloverindication is the wheel lifting detection. Thus, based on the wheellifting status using the method proposed in this disclosure, aquantitative determination of how large the wheel lift is may bedetermined, which can be used to generate brake control command.

Rolling Radius-Based Wheel Departure Roll Angle, θ_(rr-whl)

Based on the rolling radius-based wheel departure angle, a firstqualitative indication of wheel lifting may be made as one of the rollcondition detectors 64. The rolling radius r(i) of the i-th rollingwheel of a moving vehicle is related to the i-th wheel speed w_(i) (fromthe i-th ABS wheel speed sensor) and the linear corner velocity of thewheel v_(c)(i) (calculated from the steering angle, the side slip angleand the reference velocity of the vehicle) in the following equation:

$\begin{matrix}{{r(i)} = \frac{{v_{c}(i)}{R(i)}}{w(i)}} & (16)\end{matrix}$where i=0,1,2,3 implies the front-left, front-right, rear-left andrear-right wheel, and R(i) is the nominal rolling radius used to convertthe rotational speed of each wheel to a linear speed. UsuallyR(0)=R(1)=R_(f) for front wheels and R(2)=R(3)=R_(r) for rear wheels, orR(0)=R(1)=R(2)=R(3)=R₀.

The linear corner velocity is derived from the following equation:v _(c)(0)=V _(x)[ cos(δ)+tan(β)sin(δ)]+w _(z) [l _(f) sin(δ)−t _(f)cos(δ)]v _(c)(1)=V _(x)[ cos(δ)+tan(β)sin(δ)]+w _(z) [l _(f) sin(δ)+t _(f)cos(δ)]v _(c)(2)=V _(x) −w _(z) t _(r)v _(c)(3)=V _(x) +w _(z) t _(r)  (16.5)where t_(f) and t_(r) are the half tracks for the front and rear axles,l_(f) and l_(r) are the distances between the center of gravity of thevehicle and the front and rear axles, δ is the steering angle at thefront wheel, β is the side slip angle of the vehicle, w_(z) is the yawrate of the vehicle.

The front axle rolling radii-based wheel departure angle θ_(rr-whl)(0)can be computed from the rolling radii of the front-left and front-rightrolling radii in the equation

$\begin{matrix}{{\theta_{{rr} - {whl}}(0)} = {\tan^{- 1}\left\lbrack \frac{{r(0)} - {r(1)}}{t_{f}} \right\rbrack}} & (17)\end{matrix}$and the rear axle rolling radii-wheel departure angle θ_(rr-whl)(1) maybe calculated from the following equation

$\begin{matrix}{{\theta_{{rr} - {whl}}(1)} = {\tan^{- 1}\left\lbrack \frac{{r(2)} - {r(3)}}{t_{r}} \right\rbrack}} & (18)\end{matrix}$where t_(f) is the width of the front wheel track and t_(r) is the rearwheel track. Axle refers to a common axis not necessarily a fixed orphysical axle. Using formula (16), (17) and (18), the anglesθ_(rr-whl)(0) and θ_(rr-whl)(1) can be computed as in the following

if υ_(ref) > 5 for (i = 0; i < 4; + +)$\left\{ \mspace{14mu}{{{r(i)} = {{sat}\left( {\frac{{\upsilon_{c}(i)}R_{0}}{\max\left( {{w(i)},0.01} \right)},{{p\_ MAX}{\_ DRR}}} \right)}};}\mspace{14mu} \right\}$${{\theta_{{rr} - {whl}}(0)} = {{sat}\left( {\frac{{r(0)} - {r(1)}}{t_{f}},{{p\_ MAX}{\_ WDA}}} \right)}};$${{\theta_{{rr} - {whl}}(1)} = {{sat}\left( {\frac{{r(2)} - {r(3)}}{t_{f}},{{p\_ MAX}{\_ WDA}}} \right)}};$} else { θ_(rr−whl)(0) = 0; θ_(rr−whl)(1) = 0; }where p_MAX_DRR (for example, 1000) is the allowed maximum dynamicrolling radius, and p_MAX_WDA (for example, 13 degree) is the maximumrolling radius based wheel departure angle.

Notice that the above deviation assumes that the wheel has negativeslip, i.e., there are braking torques applied to the wheels. In the casethere are positive torques applied to the wheels, a negative sign isneeded. The system is passive in a sense that a change in torque is notpurposely applied as an active actuator command and it is a quantitypassively received or observed. That is, the engine operating inputtorque is used.

if (τ_(active)(0) > 0 & & τ_(active)(1) > 0) {  θ_(rr-whl)(0) =−θ_(rr-whl)(0); } if (τ_(active)(2) > 0 & & τ_(active)(3) > 0) { θ_(rr-whl)(1) = −θ_(rr-whl)(1); }where τ_(active)(i) denotes the observed torque applied to the ithwheel, which could be either a driving torque or a braking torque, orsay τ_(active)(i)=τ_(driving)(i)−τ_(braking)(i).

Notice that the above computation provides accurate captures for thefront and rear wheel axle departure angle if the involved two wheelshave zero or small longitudinal slip ratio (by comparing a calculatedlongitudinal slip ratio to a longitudinal slip ratio threshold. In thecase when a large wheel longitudinal slip is experienced, theafore-mentioned computations are no longer very accurate. However, theymay still be used to identify a significant slip difference between leftand right wheels. If one of the involved wheels has large slip ratio(for example, its wheel speed is close to zero), the computation of (17)or (18) will amplify the wheel departure angle (very large wheeldeparture angle up to 90 degree, this is not the true wheel departureangle). If both the involved wheels have the similar but large slipratios, (17) or (18) will still be small, implying grounded wheels forboth left and right sides.

Thus, the computation as in (17) or (18) provides accurate descriptionof wheel departure angle (wheel roll angle) from the average roadsurface if the wheels do not experience large longitudinal slip; itprovides amplified characterization when the involved left and rightwheels have significant slip differences.

Longitudinal Wheel Slip Ratio

Another way in which to passively detect wheel lift in one of the rollcondition detectors 64 uses longitudinal wheel slip ratio. Longitudinalwheel slip may be used to generate a second qualitative indication ofwheel lift.

The slip power is defined as the product of the slip ratio and the timederivative of the slip ratio. The longitudinal slip ratio is the ratioof the

$\frac{{wheel}\mspace{14mu}{speed}}{{vehicle}\mspace{14mu}{speed}} = {{vehicle}\mspace{14mu}{{speed}.}}$The vehicle speed may be the vehicle speed at the corner of the vehicleas described below. If the ith wheel slip is denoted as s(i) fori=0,1,2,3, then

$\begin{matrix}{{s_{p}(i)} = {{s(i)}{\frac{\mathbb{d}{s(i)}}{\mathbb{d}t}.}}} & (19)\end{matrix}$

The calculated slip power s_(p) reflects the magnitude variation of thewheel slip ratio with respect to time

$\quad\begin{matrix}\begin{matrix}{{\frac{\mathbb{d}}{\mathbb{d}t}\left\lbrack {s(i)} \right\rbrack}^{2} = {2{s(i)}\frac{\mathbb{d}{s(i)}}{\mathbb{d}t}}} \\{= {2{{s_{p}(i)}.}}}\end{matrix} & (20)\end{matrix}$

Therefore, positive slip power implies divergent wheel slip (magnitudeof slip ratio is increased), negative slip power indicates a convergentslip ratio (the magnitude of slip ratio is decreased), zero slip powerimplies that the slip ratio is kept constant. Since during wheellifting, both braking torque and driving torque will generate divergentslip for the wheel, hence positive slip power is expected. While in thecase of wheel touch-down or a grounded wheel, convergent wheel slip(negative slip power) is expected.

for (i = 0; i < 4; i + +) {  ds(i) = p_10HZ_COEF *  ds(i) + (s(i) −z1_s(i)) * (1 − p_10HZ_COEF) /0.007;  z1_s(i) = s(i) ; }where p_(—)10 HZ_COEF (for example, 0.9) is the coefficient reflecting alow-pass filter with 10 Hz cut-off frequency.

Thus, wheel slip power provides a real-time characterization of thetrend of the wheel slips during transient wheel speed changes to providea qualitative indication of wheel lifting and thus a wheel lift signal.

Slip Rate Wheel Lift

The roll condition or wheel lift of the vehicle can also be seenindirectly from the wheel longitudinal slip rate. If during a normalbraking or driving torque the wheels at one side of the vehicleexperience an increased magnitude of slip rate, then the wheels arelosing longitudinal road torque. This implies that the wheels are eitherdriven on a low mu surface or lifted up. Thus, the longitudinal sliprate s_(r) may be used in a determination of torque based qualitativedetermination of the wheel lifting.

The slip rate is defined as the product of the corner velocity and thetime derivative of the slip ratio for the ith wheel, i.e.,

$\begin{matrix}{{s_{r}(i)} = {{v_{c}(i)}{\frac{\mathbb{d}{s(i)}}{\mathbb{d}t}.}}} & (21)\end{matrix}$

Thus calculated slip rate is related to wheel acceleration

$\begin{matrix}\begin{matrix}{{\frac{\mathbb{d}}{\mathbb{d}t}{w(i)}} = {\frac{\mathbb{d}}{\mathbb{d}t}\left\{ {{v_{c}(i)}\left\lbrack {{s(i)} + 1} \right\rbrack} \right\}}} \\{= {{s_{r}(i)} + {\left\lbrack {{s(i)} + 1} \right\rbrack{\frac{\mathbb{d}{v_{c}(i)}}{\mathbb{d}t}.}}}}\end{matrix} & (22)\end{matrix}$

Considering corner velocity v_(c)(i) is usually smooth, (22) can besimplified to

$\begin{matrix}{{\frac{\mathbb{d}}{\mathbb{d}t}{w(i)}} \approx {{s_{r}(i)}.}} & (23)\end{matrix}$

Hence slip rate is a characterization of the wheel acceleration but withcomputation advantage, i.e., smoothness. Notice that during transientwheel speed changes, (23) is very accurate due to the fact that thewheel acceleration magnitude is much larger than the magnitude of thetime derivative of the corner velocity.

for (i = 0; i < 4; i++) {  s_(r)(i) = sat(v_(c)(i) *ds(i),−p_MAX_SLIP_RATE,  p_MAX_SLIP_RATE); }where p_MAX_SLIP_RATE (for example, 300) is the upper bound for limitingslip rate. Thus, as can be seen from the above formula, slip rate can bedetermined within bounds of the p_MAX_SLIP_RATE using equation (21). Theslip rate is compared to a threshold. If the slip rate increases above aslip rate threshold, then the wheel may be possibly lifted.

As will be further described below, the calculated wheel slip rate mayalso be used to compute the actual torques applied to each wheel.

Wheel Lift Using Normal Loading

The roll condition of the vehicle can also be characterized by thenormal loading sustained at each wheel. Theoretically, the normalloading of a wheel decreasing to or near zero indicates that the wheelis no longer contacting the road surface. In this case a potentialrollover is under the way. Large magnitude of this loading indicatesthat the wheel is grounded.

Normal loading is also used in a torque based wheel lift determinationas described below. The normal loading as used herein is the dynamicnormal loading, which is experienced by any of the four wheels duringvehicle dynamic maneuvers. Those normal loadings are measured along thenormal directions of the contact patches, which are the areas where thewheels and the road surface meets. If the vehicle is driven on a levelground, then the normal loadings are located at the contact patchesbetween the road and the wheels, and are perpendicular to the roadsurface.

The defined dynamic normal loading of each wheel consists of twoportions: the portion due to the heave motion of the vehicle (denoted asN_(heave)) and the portion due to the other motions of the vehicle(denoted as N_(non-heave)). That is, the total normal loading at eachwheel (denoted as N_(total)) is the sum of N_(heave) and N_(non-heave).

The heave motion generated normal loading can be calculated as thefollowing

$\begin{matrix}\begin{matrix}\begin{matrix}{{N_{heave}(0)} = {N_{heave}(1)}} \\{= {{Ma}_{z}\mspace{11mu}{\cos\left( \theta_{xr} \right)}\mspace{11mu}{\cos\left( \theta_{yr} \right)}\frac{l_{r}}{2\left( {l_{f} + l_{r}} \right)}}}\end{matrix} \\\begin{matrix}{{N_{heave}(2)} = {N_{heave}(3)}} \\{= {{Ma}_{z}{\cos\left( \theta_{xr} \right)}\mspace{11mu}{\cos\left( \theta_{yr} \right)}\frac{l_{f}}{2\left( {l_{f} + l_{r}} \right)}}}\end{matrix}\end{matrix} & (24)\end{matrix}$where a_(z) is a vertical acceleration signal from the verticalacceleration sensor 33 that may be mounted on the vehicle body but atthe center of gravity of the vehicle; M is the total mass of thevehicle; θ_(xr) is the relative roll angle between the vehicle body andthe axle of the wheels that is derived from the roll rate sensor; θ_(yr)is the relative pitch angle between the vehicle body and the roadsurface that is derived from the pitch rate sensor; l_(f) is thedistance of the vehicle center of gravity from the front axle, and l_(r)is the distance of the vehicle center of gravity from the rear axle.

The non-heave motion portion of the normal loadings are due to the othermotion of the vehicle, including the roll and pitch angular motion ofthe vehicle body with respect to the road surface, the load transfersdue to the longitudinal and lateral accelerations, which can becalculated as in the followingN _(non-heave)(0)=K _(f)(−θ_(xr) t _(f)+θ_(yr) l_(f))cos(θ_(xr))cos(θ_(yr))N _(non-heave)(1)=K _(f)(θ_(xr) t _(f)+θ_(yr) l_(f))cos(θ_(xr))cos(θ_(yr))N _(non-heave)(2)=K _(r)(−θ_(xr) t _(r)−θ_(yr) l_(r))cos(θ_(xr))cos(θ_(yr))N _(non-heave)(3)=K _(r)(θ_(xr) t _(r) −θ _(yr) l_(r))cos(θ_(xr))cos(θ_(yr))  (25)where K_(f) is the spring rate of the front suspensions and K_(r) is thespring rate of the rear suspensions.

Consequently, the total normal loadings at the wheels can be expressedas the following

$\begin{matrix}\begin{matrix}{{N_{total}(0)} = {{{Ma}_{z}\mspace{11mu}{\cos\left( \theta_{xr} \right)}\mspace{11mu}{\cos\left( \theta_{yr} \right)}\frac{l_{r}}{2\left( {l_{f} + l_{r}} \right)}} + {{K_{f}\left( {{{- \theta_{xr}}t_{f}} + {\theta_{yr}l_{f}}} \right)}\mspace{11mu}{\cos\left( \theta_{xr} \right)}\mspace{11mu}{\cos\left( \theta_{yr} \right)}}}} \\\begin{matrix}{{N_{total}(1)} = {{{Ma}_{z}\mspace{11mu}{\cos\left( \theta_{xr} \right)}\mspace{11mu}{\cos\left( \theta_{yr} \right)}\frac{l_{r}}{2\left( {l_{f} + l_{r}} \right)}} + {{K_{f}\left( {{\theta_{xr}t_{f}} + {\theta_{yr}l_{f}}} \right)}\mspace{11mu}{\cos\left( \theta_{xr} \right)}\mspace{11mu}{\cos\left( \theta_{yr} \right)}}}} \\\begin{matrix}{{N_{total}(2)} = {{{Ma}_{z}\mspace{11mu}{\cos\left( \theta_{xr} \right)}\mspace{11mu}{\cos\left( \theta_{yr} \right)}\frac{l_{f}}{2\left( {l_{f} + l_{r}} \right)}} + {{K_{r}\left( {{{- \theta_{xr}}t_{f}} - {\theta_{yr}l_{r}}} \right)}\mspace{11mu}{\cos\left( \theta_{xr} \right)}\mspace{11mu}{\cos\left( \theta_{yr} \right)}}}} \\{{N_{total}(3)} = {{{Ma}_{z}\mspace{11mu}{\cos\left( \theta_{xr} \right)}\mspace{11mu}{\cos\left( \theta_{yr} \right)}\frac{l_{f}}{2\left( {l_{f} + l_{r}} \right)}} + {{K_{r}\left( {{\theta_{xr}t_{f}} - {\theta_{yr}l_{r}}} \right)}\mspace{11mu}{\cos\left( \theta_{xr} \right)}\mspace{11mu}{\cos\left( \theta_{yr} \right)}}}}\end{matrix}\end{matrix}\end{matrix} & (26)\end{matrix}$

If in case the heave motion of the vehicle is negligible, i.e., theheave acceleration of the vehicle is small. Then the verticalacceleration sensor output should be close to the gravity, i.e.a_(z)≈g  (27)

In this case an approximation of the normal loadings can be written asthe following

$\begin{matrix}{{{N_{total}(0)} \approx {{{Mg}\frac{l_{r}}{2\left( {l_{f} + l_{r}} \right)}} + {K_{f}\left( {{{- \theta_{xr}}t_{f}} + {\theta_{yr}l_{f}}} \right)}}}{{N_{total}(1)} \approx {{{Mg}\frac{l_{r}}{2\left( {l_{f} + l_{r}} \right)}} + {K_{f}\left( {{\theta_{xr}t_{f}} + {\theta_{yr}l_{f}}} \right)}}}{{N_{total}(2)} \approx {{{Mg}\frac{l_{f}}{2\left( {l_{f} + l_{r}} \right)}} + {K_{r}\left( {{{- \theta_{xr}}t_{r}} - {\theta_{yr}l_{r}}} \right)}}}{{N_{total}(3)} \approx {{{Mg}\frac{l_{f}}{2\left( {l_{f} + l_{r}} \right)}} + {{K_{r}\left( {{\theta_{xr}t_{r}} - {\theta_{yr}l_{r}}} \right)}.}}}} & (28)\end{matrix}$

The calculated normal loadings provide an indication of wheel liftabove. When the normal load is near zero, this provides an indication ofwheel lift. The normal loads are thus compared to a normal loadthreshold. When the normal loads are lower (below the threshold) or nearzero, the wheel has lifted. The normal loadings may also be used tocompute the road torques described below.

Wheel Lift Using Road Torque

The roll condition or wheel lift can also be identified by checking theactual road torques applied to the wheels and the road torques, whichare needed to sustain the wheels when the wheels are grounded. Theactual road torques can be obtained through torque balancing for eachwheel using wheel acceleration, driving torque and braking torque. Ifthe wheel is contacting the road surface, the calculated actual roadtorques must match or be larger than the nonlinear torques calculatedfrom the normal loading and the longitudinal slip at each wheel.

The actual road torques τ_(road) applied to the wheel together with thedriving torque τ_(d), braking torque τ_(d) and the wheel rotationinertia I_(w) obey the following Newton's law

$\begin{matrix}{{{I_{wf}{\frac{\mathbb{d}}{\mathbb{d}t}\left\lbrack \frac{{WhlSpd}(0)}{R_{0f}} \right\rbrack}} = {{\tau_{d}(0)} - {\tau_{b}(0)} - {\tau_{road}(0)}}}{{I_{wf}{\frac{\mathbb{d}}{\mathbb{d}t}\left\lbrack \frac{{WhlSpd}(1)}{R_{0f}} \right\rbrack}} = {{\tau_{d}(1)} - {\tau_{b}(1)} - {\tau_{road}(1)}}}{{I_{wr}{\frac{\mathbb{d}}{\mathbb{d}t}\left\lbrack \frac{{WhlSpd}(2)}{R_{0r}} \right\rbrack}} = {{\tau_{d}(2)} - {\tau_{b}(2)} - {\tau_{road}(2)}}}{{I_{wr}{\frac{\mathbb{d}}{\mathbb{d}t}\left\lbrack \frac{{WhlSpd}(3)}{R_{0r}} \right\rbrack}} = {{\tau_{d}(3)} - {\tau_{b}(3)} - {{\tau_{road}(3)}.}}}} & (29)\end{matrix}$

Using equations (23), (29) the road torques may be calculated in

$\begin{matrix}{{{\tau_{road}(0)} \approx {{\tau_{d}(0)} - {\tau_{b}(0)} - {I_{wf}\frac{s_{r}(0)}{R_{0f}}}}}{{\tau_{road}(1)} \approx {{\tau_{d}(1)} - {\tau_{b}(1)} - {I_{wf}\frac{s_{r}(1)}{R_{0f}}}}}{{\tau_{road}(2)} \approx {{\tau_{d}(2)} - {\tau_{b}(2)} - {I_{wr}\frac{s_{r}(2)}{R_{0f}}}}}{\tau_{road}(3)} \approx {{\tau_{d}(3)} - {\tau_{b}(3)} - {I_{wr}\frac{s_{r}(3)}{R_{0f}}}}} & (30)\end{matrix}$

Road Torque When the Wheel is Grounded

If the wheel is grounded, i.e., contacting the road surface, then thegrounded road torque τ_(road-grd)(i) is related to the wheel slip ratios(i), the wheel side slip angle α(i) and the wheel dynamic normalloading N_(total)(i) through a nonlinear functional relationship as inthe followingτ_(road-grd)(i)=N _(total)(i)φ(s(i),α(i)).  (31)

A linearization for the nonlinear function φ(•, •) could be obtained asthe followingφ(s(i), α(i))=κ(α(i))s(i).  (32)

If the wheel side slip angle is small, equation (30) could beapproximated as the followingτ_(road-grd)(i)≈κ(i)N_(total)(i)s(i)  (33)where κ(i) is the initial slope of the function κ(α(i)). Theapproximation (33) can be implemented as in the following

$\begin{matrix}{{{for}\mspace{11mu}\left( {{i = 0};{i < 4};{i++}} \right)}\left\{ \mspace{14mu}{{if}\mspace{11mu}\left( {{{s(i)} \leq 0}\&\&\mspace{11mu}{{s(i)} \geq {{p\_ BRAKING}{\_ LIN}{\_ SLIP}\mspace{14mu}{}\mspace{14mu}{s(i)}} \geq 0}\&\&\mspace{11mu}{{s(i)} \leq {{p\_ DRIVING}{\_ LIN}{\_ SLIP}}}}\mspace{11mu} \right)\mspace{14mu}\left\{ \mspace{14mu}{{{\tau_{{road} - {grd}}(i)} = {{N_{total}(i)}*{p\_ SLIP}{\_ TO}{\_ RT}{\_ GAIN}*{s(i)}*R_{0}}};}\mspace{14mu} \right\}\mspace{14mu}{else}\mspace{14mu}{if}\mspace{11mu}\left( {{s(i)} \leq {{p\_ BRAKING}{\_ LIN}{\_ SLIP}}}\mspace{11mu} \right)\mspace{14mu}\left\{ \mspace{14mu}{{{\tau_{{road} - {grd}}(i)} = {{N_{total}(i)}*{p\_ SLIP}{\_ TO}{\_ RT}{\_ GAIN}*{p\_ BRAKING}{\_ LIN}{\_ SLIP}*R_{0}}};}\mspace{14mu} \right\}\mspace{14mu}{else}\text{}\mspace{14mu}\left\{ \mspace{14mu}{{{\tau_{{road} - {grd}}(i)} = {{N_{total}(i)}*{p\_ SLIP}{\_ TO}{\_ RT}{\_ GAIN}*{p\_ DRIVING}{\_ LIN}{\_ SLIP}*R_{0}}};}\mspace{14mu} \right\}} \right\}} & (34)\end{matrix}$where p_BRAKING_LIN_SLIP (for example, −10%) is a braking slip thresholdand p_DRIVING_LIN_SLIP (for example, 25%) is a driving slip threshold.The thresholds are the maximum slip when the linear relationship betweenroad torque and the slip are valid during braking and driving cases.

As can be seen by the above logic, if during braking the slip ratio isless than or equal to zero and the slip ratio is greater than or equalto a braking slip threshold, or during driving the slip rate is greaterthan or equal to zero and the slip rate is less than or equal to thedriving slip threshold, the road torque can be determined by one of thethree formulas.

The following is a list of the output variables of the passive wheellift detector 58. As can be seen, the output has a plurality of levels.Each one of the wheel lift determinations may generate an outputvariable or state as will be described below. In some instances thestates are characterized in a numerical sense with “absolutely grounded”being the highest value and “no indication” as the lowest value.

Output Variables

-   -   Passive wheel lift status: PWLD(i).

If the ith wheel is absolutely grounded, thenPWLD(i)=ABSOLUTELY_GROUNDED

If the ith wheel is in the edge of grounding, PWLD(i)=POSSIBLY_GROUNDED

If the ith wheel is absolutely lifted, then PWLD(i)=ABSOLUTELY_LIFTED

If the ith wheel is in the beginning of lifting PWLD(i)=POSSIBLY_LIFTED

If the ith wheel's status cannot be firmly identified,PWLD(i)=NO_INDICATION

The following parameters are used in the determination of wheel liftingstatus.

Parameters

-   p_MAX_DRR: the upper bound for dynamic rolling radius. In this    example a value of (1000 m) was used.-   p_MAX_WDA: the upper bound for the rolling radius based wheel    departure angle. In this example a value of (13 deg) was used.-   p_ROLL_TH_(—)05=0.05*ROLL_GRADIENT-   p_ROLL_TH_(—)25=0.25*ROLL_GRADIENT-   p_ROLL_TH_(—)40=0.40*ROLL_GRADIENT-   p_ROLL_TH_(—)55=0.55*ROLL_GRADIENT-   p_ROLL_TH_(—)75=0.75*ROLL_GRADIENT-   p_STAT_NLOAD_F: the static normal loading of the front wheels (per    wheel).-   p_STAT_NLOAD_R: the static normal loading of the rear wheels (per    wheel).-   p_SLIP_RT_GAIN: the gain used to convert slip ratio to normalized    road torque. In this example a value of (6) was used.-   p_NLOAD_LOSS: the allowed percentage of normal loading loss. In this    example a value of (0.3) was used.-   p_GRD_DW_DWA_TH: the allowed wheel departure angle for grounded    driven wheel. In this example a value of (0.41 deg) was used.-   p_GRD_NDW_DWA_TH: the allowed wheel departure angle for grounded    non-driven wheel. In this example a value of (1.25 deg) was used.-   p_LFT_DW_DWA_TH: the min wheel departure angle for grounded driven    wheel to lift. In this example a value of (4 deg) was used.-   p_LFT_NDW_DWA_TH: the min wheel departure angle for grounded    non-driven wheel to lift. In this example a value of (10 deg) was    used.-   p_GRD_PR_TH: the braking pressure for grounded wheel torque    condition. In this example a value of (6 bar) was used.-   p_LFT_PR_TH: the braking pressure for lifted wheel select-low torque    condition. In this example a value of (20 bar) was used.-   p_LFT_SP_MIN_TH: the min slip power for possibly grounded condition.    In this example a value of (0.4) was used.

Comparison Logic

Various comparisons are used by the embodiment to determine thequalitative level or lack thereof of wheel lifting. The passive wheellift detector 58 sets PWLD(i) for i=0,1,2,3, where 0 represents the FLwheel, 1 represents the RL wheel, and 3 represents the RR wheel. IfPWLD(i)=ABSOLUTELY_GROUNDED, then the ith wheel is definitely contactingthe road surface; if PWLD(i)=POSSIBLY_GROUNDED, then the ith wheel isabout to contact the road surface; if PWLD(i)=ABSOLUTELY_LIFTED then theith wheel is definitely lifted or up in the air; ifPWLD(i)=POSSIBLY_LIFTED, then the ith wheel is about leaving contactingthe road surface; if PWLD(i)=NO_INDICATION, then there is no firmindication for both lifting and grounding for the ith wheel.

The roll information is first used to screen the grounding and liftingtrends of the wheels. The following rough screening uses the relativeroll angle θ_(xr) and the roll rate based wheel departure angle θ_(whl).If both the magnitudes of θ_(xr) and θ_(whl) are small, the vehiclewheels are probably grounded:

$\begin{matrix}{{{if}\mspace{11mu}\left( {\theta_{xr} > 0} \right)}\left\{ \mspace{14mu}{{if}\mspace{11mu}\left( {{\theta_{xr} \leq {{p\_ ROLL}{\_ TH}\_ 55}}\&\&{\theta_{whl} \leq {{p\_ ROLL}{\_ TH}\_ 05}}}\mspace{11mu} \right)\mspace{20mu}\left\{ \mspace{14mu}{{{{PWLD}(0)} = {{{POSSIBLY\_ GROUNDED}\mspace{31mu}{{PWLD}(2)}} = {POSSIBLY\_ GROUNDED}}};}\mspace{11mu} \right\}\mspace{31mu}{else}\mspace{20mu}\left\{ \mspace{14mu}{{{{PWLD}(0)} = {NO\_ INDICATION}};\mspace{25mu}{{{PWLD}(2)} = {NO\_ INDICATION}};}\mspace{11mu} \right\}} \right\}{else}\left\{ \mspace{14mu}{{if}\mspace{11mu}\left( {{\theta_{xr} \geq {{- {p\_ ROLL}}{\_ TH}\_ 55}}\&\&{\theta_{whl} \geq {{p\_ ROLL}{\_ TH}\_ 05}}}\mspace{11mu} \right)\mspace{14mu}\left\{ \mspace{14mu}{{{{PWLD}(1)} = {POSSIBLY\_ GROUNDED}};\mspace{25mu}{{{PWLD}(3)} = {POSSIBLY\_ GROUNDED}};}\mspace{11mu} \right\}\mspace{14mu}{else}\mspace{11mu}\left\{ \mspace{14mu}{{{{PWLD}(1)} = {NO\_ INDICATION}};\mspace{20mu}{{{PWLD}(3)} = {NO\_ INDICATION}};}\mspace{11mu} \right\}} \right\}} & (35)\end{matrix}$where p_ROLL_TH_(—)05 is the static relative roll angle corresponding to5% of the roll gradient, p_ROLL_TH_(—)55 is the static relative rollangle corresponding to 55% of the roll gradient. If both the magnitudesof θ_(xr) and θ_(whl) are large, the vehicle wheels are probably lifted.After the above first cut, a refinement for determining absolutelygrounded and absolutely lifted conditions is conducted.

The first concern is the detection of the absolutely grounded conditionfor the wheels. Several variables, including N_(total)(i), τ_(road)(i),τ_(road-grd)(i) and the rolling radii based wheel departure angleθ_(rr-whl)(0), θ_(rr-whl)(1), are used to checking whether the ith wheelis absolutely grounded. Assume that the roll angle screening throughlogic (35) indicates that the wheels of interest are possibly grounded.In order to confirm the possibly grounded wheels are actually absolutelygrounded, the following conditions are then checked. If any of thoseconditions is met, an absolutely grounded flag is set for the wheel ofinterest.

Normal loading condition: if PWLD(i)=POSSIBLY_GROUNDED and at the sametime the normal loading satisfiesN _(total)(i)≧N _(th)(i)then PWLD(i)=ABSOLUTELY_GROUNDED. Here four variables N_(th)(i) fori=0,1,2,3 are used as the minimum normal loadings for the wheels whenthey are grounded:N _(th)(0)=p_STAT_(—) NLOAD_(—) F*(1−p _(—) NLOAD_LOSS);N _(th)(1)=p_STAT_(—) NLOAD_(—) F*(1−p _(—) NLOAD_LOSS);N _(th)(2)=p_STAT_(—) NLOAD_(—) R*(1−p _(—) NLOAD_LOSS);N _(th)(3)=p_STAT_(—) NLOAD_(—) R*(1−p _(—) NLOAD_LOSS);  (36)

Slip power condition: if PWLD(i)=POSSIBLY_GROUNDED and at the same timethe slip power is negative (s_(p)(i)<0), i.e., the magnitude of the slipratio is decreasing (convergent slip ratio), then set the wheel liftflag as PWLD(i)=ABSOLUTELY_GROUNDED.

Road torque condition: if PWLD(i)=POSSIBLY_GROUNDED and at the same timethe magnitude of the actual road torque τ_(road)(i) from (30) is greaterthan the grounded wheel road torque τ_(road-grd)(i) from (33) and bothhave the same sign, orτ_(road)(i)τ_(road-grd)(i)>=0and|τ_(road)(i)|≧|τ_(road-grd)(i)|then PWLD(i)=ABSOLUTELY_GROUNDED.

Active torque condition: if PWLD(i)=POSSIBLY_GROUNDED, and at the sametime the active torque (either braking torque or driving torque) appliedto the ith wheel is larger enough while the wheel departure anglegenerated from rolling radii θ_(rr-whl)(j) for j=0,1 is small enough,then the ith wheel is deemed to be absolutely grounded. Notice that thethresholds for driven wheels and non-driven wheels are different.

The following logic is a summary of the above discussion for the casewhere the vehicle is turned left and the left side of the vehicle hasthe potential trend to lift up.

$\begin{matrix}{{{{if}\mspace{14mu}\theta_{xr}} > 0}\left\{ \mspace{14mu}{{if}\mspace{11mu}\left( \mspace{14mu}{{{{PLWD}(0)}=={POSSIBLY\_ GROUNDED}}\mspace{25mu}\&\&\left( \mspace{14mu}{{N_{total}(0)} \geq {{N_{th}(0)}\mspace{79mu}{}{s_{p}(0)}} < {0\mspace{79mu}{}\left( {{{{{\tau_{road}(0)}*{\tau_{{road} - {grd}}(0)}} \geq 0}\&\&}❘{{\tau_{road}(0)}{ \geq }{\tau_{{road} - {grd}}(0)}}} \right)\mspace{79mu}{}\left( {{{{\theta_{{rr} - {whl}}(0)}} \leq {{p\_ GRD}{\_ DW}{\_ DWA}{\_ TH}}}\&\&\mspace{11mu}{{P_{\tau}(0)}==2}\&\&{{{\tau_{active}(0)}} \geq {{p\_ GRD}{\_ PR}{\_ TH}*{BRKTQ\_ GAIN}{\_ F}}}} \right)\mspace{79mu}{}\left( {{\theta_{{rr} - {whl}}(0)}❘{{{\leq {{p\_ GRD}{\_ NDW}{\_ DWA}{\_ TH}}}\&\&\mspace{11mu}{{P_{\tau}(0)}!=2}\&\&\mspace{11mu}{\tau_{active}(0)}}❘{\geq {{p\_ GRD}{\_ PR}{\_ TH}*{BRKTQ\_ GAIN}{\_ F}}}}} \right)}}\mspace{11mu} \right)}\mspace{14mu} \right)\left\{ \mspace{20mu}{{{{PWLD}(0)} = {ABSOLUTELY\_ GROUNDED}};}\mspace{14mu} \right\}{if}\mspace{14mu}\left( \mspace{11mu}{{{{PLWD}(2)}=={POSSIBLY\_ GROUNDED}}\mspace{20mu}\&\&\left( {{N_{total}(2)} \geq {{N_{th}(2)}\mspace{76mu}{}{s_{p}(2)}} < {0\mspace{76mu}{}\left( {{{{{\tau_{road}(2)}*{\tau_{{total} - {grd}}(2)}} \geq 0}\&\&}❘{{\tau_{road}(2)}{ \geq }{\tau_{{road} - {grd}}(2)}}} \right)\mspace{76mu}{}\left( {{{{\theta_{{rr} - {whl}}(1)}} \leq {{p\_ GRD}{\_ DW}{\_ DWA}{\_ TH}}}\&\&\mspace{11mu}{{P_{\tau}(2)}==2}\&\&{{{\tau_{active}(2)}} \geq {{p\_ GRD}{\_ PR}{\_ TH}*{BRKTQ\_ GAIN}{\_ R}}}} \right)\mspace{76mu}{}\left( {{\theta_{{rr} - {whl}}(1)}❘{{{\leq {{p\_ GRD}{\_ NDW}{\_ DWA}{\_ TH}}}\&\&\mspace{14mu}{{P_{\tau}(0)}!=2}\mspace{85mu}\&\&\mspace{11mu}{\tau_{active}(2)}}❘{\geq {{p\_ GRD}{\_ PR}{\_ TH}*{BRKTQ\_ GAIN}{\_ R}}}}} \right)}}\mspace{11mu} \right)}\mspace{14mu} \right)\left\{ \mspace{14mu}{{{{PWLD}(2)} = {ABSOLUTELY\_ GROUNDED}};}\mspace{14mu} \right\}} \right\}} & (37)\end{matrix}$

If the vehicle is turned to the right, then the following logic is usedfor detecting an absolutely grounded condition

$\begin{matrix}\begin{matrix}{{{if}\mspace{14mu}\theta_{\;{xr}}} \leq 0} \\\left\{ {{if}\mspace{14mu}\left( {{{PLWD}(1)}=={POSSIBLY\_ GROUNDED}} \right.} \right. \\{\mspace{25mu}{\&\&\;\left( {{N_{\;{total}}(1)} \geq {N_{\;{th}}(1)}} \right.}} \\{\mspace{50mu}\left. ||{{s_{\; p}(1)} < 0} \right.} \\{\mspace{50mu}\left. ||\left( {{{{\tau_{\;{road}}(1)}*{\tau_{\;{{road}\;\text{-}\;{grd}}}(1)}} \geq 0}\;\&\&}\mspace{11mu} \middle| {\tau_{\;{road}}(1)} \middle| {\geq \left| {\tau_{\;{{road}\;\text{-}\;{grd}}}(1)} \right.} \right) \right.} \\{\mspace{50mu}\left. ||\left( {{{{\theta_{\;{{rr}\text{-}{whl}}}(0)}} \leq {{p\_ DW}{\_ DWA}{\_ TH}}}\;\&\&\mspace{11mu}{{P_{\;\tau}(1)}==2}} \right. \right.} \\\left. \mspace{76mu}{\&\&\mspace{11mu}{{{\tau_{\;{active}}(1)}} \geq {{p\_ GRD}{\_ PR}{\_ TH}*{BRKTQ\_ GAIN}{\_ F}}}} \right) \\{\mspace{50mu}\left. ||\left( {\theta_{{rr}\text{-}{whl}}(1)} \middle| {{\leq {{p\_ NDW}{\_ DWA}{\_ TH}}}\;\&\&\mspace{11mu}{{P_{\tau}(1)}!=2}} \right. \right.} \\\left. \left. \left. \mspace{76mu}\left. {\&\&\mspace{14mu}{\tau_{active}(1)}} \middle| {\geq {{p\_ GRD}{\_ PR}{\_ TH}*{BRKTQ\_ GAIN}{\_ F}}} \right. \right) \right) \right) \\{\mspace{25mu}\left\{ {{{{PWLD}(1)} = {ABSOLUTELY\_ GROUNDED}};} \right\}} \\{\mspace{25mu}{{if}\mspace{14mu}\left( {{{PLWD}(3)}=={POSSIBLY\_ GROUNDED}} \right.}} \\{\mspace{50mu}{\&\&\;\left( {{N_{total}(3)} \geq {N_{th}(3)}} \right.}} \\{\mspace{76mu}\left. ||{{s_{p}(3)} < 0} \right.} \\{\mspace{76mu}\left. ||\left( {{{{\tau_{road}(3)}*{\tau_{{road}\text{-}{grd}}(3)}} \geq 0}\;\&\&}\mspace{11mu} \middle| {\tau_{road}(3)} \middle| {\geq \left| {\tau_{{road}\;\text{-}\;{grd}}(3)} \right.} \right) \right.} \\{\mspace{76mu}\left. ||\left( \left| {\theta_{{rr}\text{-}{whl}}(1)} \middle| {{\leq {{p\_ DW}{\_ DWA}{\_ TH}}}\;\&\&\mspace{11mu}{{P_{\tau}(3)}==2}} \right. \right. \right.} \\\left. \mspace{101mu}{\&\&\;\left| {\tau_{active}(3)} \middle| {\geq {{p\_ GRD}{\_ PR}{\_ TH}*{BRKTQ\_ GAIN}{\_ R}}} \right.} \right) \\{\mspace{76mu}\left. ||\left( {\theta_{{rr}\text{-}{whl}}(1)} \middle| {{\leq {{p\_ NDW}{\_ DWA}{\_ TH}}}\;\&\&\mspace{11mu}{{P_{\tau}(3)}!=2}} \right. \right.} \\\left. \left. \left. \mspace{101mu}\left. {\&\&\;{\tau_{active}(3)}} \middle| {\geq {{p\_ GRD}{\_ PR}{\_ TH}*{BRKTQ\_ GAIN}{\_ R}}} \right. \right) \right) \right) \\{\mspace{25mu}\left\{ {{{{PWLD}(3)} = {ABSOLUTELY\_ GROUNDED}};} \right\}} \\\}\end{matrix} & (38)\end{matrix}$where the torque BRKTQ_GAIN_F and BRKTQ_GAIN_R are two parameters usedto convert the braking pressure at the front and rear wheels to thebraking torque applied to the front and rear wheels; p_PRESS_TH denotesthe pressure used to set threshold for active torques.

Notice that the four variables P_(τ)(i) for i=0,1,2,3 are used in thelogic (38) and (39), which are called the torque pattern variables.P_(τ)(i)s are used to identify the torque patterns where the meaningfulwheel lifting information can be identified. This torque patterningincludes positive torques for both left and right side in the front orthe rear axle; negative torques for both left and right side in thefront or the rear axle. In order to eliminate the wheel slip differencedue to significant torque difference between the left and right wheels,the lower of two values is selected. These values are (1) the torqueapplied to the current wheel of interest, and (2) the torque applied tothe other wheel on the same axle plus the torque generated from 20 barof brake pressureP _(τ)(0)=τ_(active)(0)≦0 && τ_(active)(1)≦0&&|τ_(active)(0)|≦|τ_(active)(1)|+p _(—) LFT _(—) PR _(—)TH*BRKTQ_GAIN_(—) F+(τ_(active)(0)>0 && τ_(active)(1)>0&&|τ_(active)(0)|≦|τ_(active)(1)|+p _(—) LFT _(—) PR _(—)TH*BRKTQ_GAIN_(—) F)*2;P _(τ)(2)=τ_(active)(2)≦0 && τ_(active)(3)≦0&&|τ_(active)(2)|≦|τ_(active)(3)|+p _(—) LFT _(—) PR _(—)TH*BRKTQ_GAIN_(—) R+(τ_(active)(2)>0 && τ_(active)(3)>0 &&τ_(active)(2)|≦|τ_(active)(3)|+p _(—) LFT _(—) PR _(—) TH*BRKTQ_GAIN_(—)R)*2;P _(τ)(1)=τ_(active)(1)≦0 && τ_(active)(0)≦0&&|τ_(active)(1)|≦|τ_(active)(0)|+p _(—) LFT _(—) PR _(—)TH*BRKTQ_GAIN_(—) F+(τ_(active)(1)>0 && τ_(active)(0)>0&&|τ_(active)(1)|≦|τ_(active)(0)|+p _(—) LFT _(—) PR _(—)TH*BRKTQ_GAIN_(—) F)*2;P _(τ)(3)=τ_(active)(3)≦0 && τ_(active)(2)≦0&&|τ_(active)(3)|≦|τ_(active)(2)|+p _(—) LFT _(—) PR _(—)TH*BRKTQ_GAIN_(—) R+(τ_(active)(3)>0 && τ_(active)(2)>0&&|τ_(active)(3)|≦|τ_(active)(2)|+p _(—) LFT _(—) PR _(—)TH*BRKTQ_GAIN_(—) R)*2;  (39)

Now the wheels are checked for a lifted condition. Assume the initialroll information screening as through logic (35) indicates a wheel ofinterest as no indication, then the wheel is probably in the liftingtrend. In this case further roll condition screening for potentiallifting is conducted

$\begin{matrix}\begin{matrix}{{{if}\mspace{14mu}\theta_{x\; r}} > 0} \\\left\{ {\theta_{cond} = \left( {\theta_{xr} \geq {{p\_ ROLL}{\_ TH}\_ 75}} \right.} \right. \\{\mspace{50mu}\left. ||\left( {{\theta_{xr} \geq {{p\_ ROLL}{\_ TH}\_ 50}}\;\&\&\mspace{11mu}{\theta_{whl} \geq {{p\_ ROLL}{\_ TH}\_ 25}}} \right) \right.} \\\left. {\left. \mspace{50mu}\left. ||\left( {{\theta_{xr} \geq {{p\_ ROLL}{\_ TH}\_ 40}}\;\&\&\mspace{11mu}{\theta_{whl} \geq {{p\_ ROLL}{\_ TH}\_ 75}}} \right) \right. \right);} \right\} \\{else} \\\left\{ {\theta_{cond} = \left( {\theta_{xr} \leq {{- {p\_ ROLL}}{\_ TH}\_ 75}} \right.} \right. \\{\mspace{50mu}\left. ||\left( {{\theta_{xr} \leq {{- {p\_ ROLL}}{\_ TH}\_ 50}}\;\&\&\mspace{11mu}{\theta_{whl} \leq {{- {p\_ ROLL}}{\_ TH}\_ 25}}} \right) \right.} \\{\left. \mspace{50mu}\left. ||\left( {{\theta_{xr} \leq {{- {p\_ ROLL}}{\_ TH}\_ 40}}\;\&\&\mspace{11mu}{\theta_{whl} \leq {{- {p\_ ROLL}}{\_ TH}\_ 75}}} \right) \right. \right);} \\\}\end{matrix} & (40)\end{matrix}$where p_ROLL_TH_(—)75, p_ROLL_TH_(—)50, p_ROLL_TH_(—)40 andp_ROLL_TH_(—)25 are the static relative roll angle corresponding to 75%,50%, 40% and 25% of the roll gradient. If the above roll screeningcondition θ_(cond)==1, then the first cut for lifting detection isobtained. Notice that the actual wheel departure angle θ_(whl)(calculated from the roll rate sensor) is different from the rollingradius based wheel departure angle θ_(rr-whl)(0) (for front wheels) andθ_(rr-whl)(1) (for rear wheels). As in the grounding wheel detection,further confirmation is needed to obtain absolutely lifted condition.Let PL_(cond)(i) be the possibly lifted flags for the ith wheel, it canbe calculated based on the following two conditions which reflectpossibly lifted conditions:

Slip power condition: if the slip power of the ith wheel s_(p)(i)≧0indicates that this wheel has a divergent slip ratio, i.e., themagnitude of the slip ratio is increasing. (Considering potentialnon-braking drag on the wheels, a small negative number is used insteadof 0 is used, i.e., we use s_(p)(i)≧−0.01 to replace s_(p)(i)≧0).

Normal loading condition: if the ith normal load N_(total)(i) is smallerthan a constant threshold, then the ith wheel is possibly lifted;

For positive relative roll angle, PL_(cond)(0) and PL_(cond)(2) arecalculated as in the following

$\begin{matrix}\begin{matrix}{{{if}\mspace{14mu}\theta_{xr}} > 0} \\\{ \\{\mspace{25mu}{{{{PL}_{cond}(0)} = {{{s_{p}(0)} \geq {- 0.01}}\;\&\&\;\left( {\theta_{cond}==1}||{{N_{total}(0)} \leq {{p\_ LOAD}{\_ F}*{p\_ LOSS}}} \right)}};}} \\{\mspace{25mu}{{{{PL}_{cond}(2)} = {{{s_{p}(2)} \geq {- 0.01}}\;\&\&\;\left( {\theta_{cond}==1}||{{N_{total}(2)} \leq {{p\_ LOAD}{\_ R}*{p\_ LOSS}}} \right)}};}} \\\}\end{matrix} & (41)\end{matrix}$

If the relative roll angle θ_(xr) is negative, PL_(cond)(1) andPL_(cond)(3) can be calculated as in the following

$\begin{matrix}\begin{matrix}{{{if}\mspace{14mu}\theta_{xr}} \leq 0} \\\{ \\{\mspace{25mu}{{{{PL}_{cond}(1)} = {{{s_{p}(1)} \geq {- 0.01}}\;\&\&\;\left( {\theta_{cond}==1}||{{N_{total}(1)} \leq {{p\_ LOAD}{\_ F}*{p\_ LOSS}}} \right)}};}} \\{\mspace{25mu}{{{{PL}_{cond}(3)} = {{{s_{p}(3)} \geq {- 0.01}}\;\&\&\;\left( {\theta_{cond}==1}||{{N_{total}(3)} \leq {{p\_ LOAD}{\_ R}*{p\_ LOSS}}} \right)}};}} \\\}\end{matrix} & (42)\end{matrix}$

Using the calculated condition flags, PL_(cond)(i) will be used to setpossibly lifted status of wheels

$\begin{matrix}\begin{matrix}{{for}\mspace{14mu}\left( {{i = 0};{i < 4};{i++}} \right)} \\\{ \\\left. \mspace{25mu}{{{if}\mspace{14mu}{{PL}_{cond}(i)}}==1} \right) \\{\mspace{50mu}{{{{PWLD}(i)} = {POSSIBLY\_ LIFTED}};}} \\\}\end{matrix} & (43)\end{matrix}$

Now the absolutely lifted conditions are determined. In the following weassume the wheels are already in possibly lifted status through (42).

Torque Select-Low Condition for Non-Driven Wheel

In this case, if the applied braking torque satisfied the torque patterncondition, i.e., for the right loaded wheel caseτ_(active)(left)≧τ_(active)(right)−p _(—) PRES _(—) SL _(—)TH*BRKTQ_GAIN  (44)and for left loaded wheel caseτ_(active)(right)≧τ_(active)(left)−p _(—) PRES _(—) SL _(—)TH*BRKTQ_GAIN  (45)then the wheel lifting will be checked with the rolling radius basedwheel departure angle condition for front wheels|θ_(rr-whl)(0)|≧p _(—) NDW _(—) WDA _(—) TH  (46)and for rear wheelsθ_(rr-whl)(1)|≧p _(—) NDW _(—) WDA _(—) TH  (47)where the threshold p_NWD_WDA_TH is the threshold for non-driven wheel'srolling radius based wheel departure angle.

Torque Select-Low Condition for Driven Wheel During Engine Braking

In this case torque select-low condition is the same as (29) and (30),but the wheel departure angle conditions needs to use differentthreshold. For right-loaded wheel case|θ_(rr-whl)(0)|≧p _(—) DW _(—) WDA _(—) TH  (48)and for rear wheels|θ_(rr-whl)(1)|≧p _(—) DW _(—) WDA _(—) TH  (49)

Torque Select-Low Condition for Driven Wheel During Engine Driving

In this case, the torque select-low condition is the same as thefollowing for the right loaded wheelτ_(active)(left)≦τ_(active)(right)+p _(—) PRES _(—) SL _(—)TH*BRKTQ_GAIN  (50)and for left loaded wheel caseτ_(active)(right)≦τ_(active)(left)+p _(—) PRES _(—) SL _(—)TH*BRKTQ_GAIN  (51)

A detailed logic can be summarized as the following for the rightedloaded wheel case:

$\begin{matrix}\begin{matrix}{{{if}\mspace{14mu}\theta_{xr}} > 0} \\\{ \\{\mspace{25mu}{{if}\mspace{14mu}\left( {{{{PWLD}(0)}=={NO\_ INDICATION}}\;\&\&\mspace{11mu}{{{PWLD}(0)}=={POSSIBLY\_ LIFTED}}} \right)}} \\{\mspace{25mu}\{} \\{\mspace{50mu}{{if}{~~}\left( {{{P_{\tau}(0)}==1}\;\&\&\mspace{11mu}{{\theta_{{rr}\text{-}{whl}}(0)} \geq {{p\_ LFT}{\_ NDW}{\_ WDA}{\_ TH}}}} \right.}} \\{\mspace{50mu}\left. ||{{{P_{\tau}(0)}==2}\;\&\&\mspace{11mu}{{\theta_{{rr}\text{-}{whl}}(0)} \geq {{p\_ LFT}{\_ DW}{\_ WDA}{\_ TH}}}} \right.} \\{\mspace{50mu}\left. ||{{{P_{\tau}(0)}==1}\;\&\&\mspace{11mu}{{\theta_{{rr}\text{-}{whl}}(0)} \geq {{p\_ LFT}{\_ DW}{\_ WDA}{\_ TH}}}} \right.} \\{\mspace{50mu}{\&\&\;\left( \left. {{DRIVE\_ MODE}=={FRONT}}||{{DRIVE\_ MODE}=={FOUR}} \right.|| \right.}} \\\left. \left. \mspace{149mu}{{DRIVE\_ MODE}=={TOD}} \right) \right) \\\left. \mspace{76mu} \right) \\{\mspace{50mu}\left\{ {{{{PWLD}\lbrack 0\rbrack} = {ABSOLUTELY\_ LIFTED}};} \right\}} \\{\mspace{50mu}{{if}\mspace{14mu}\left( {{s_{p}(0)} \leq {{- {p\_ LFT}}{\_ SP}{\_ MIN}{\_ TH}}} \right)}} \\{\mspace{50mu}\left\{ {{{{PWLD}\lbrack 0\rbrack} = {POSSIBLY\_ GROUNDED}};} \right\}} \\\left. \mspace{25mu} \right\} \\\left. {{\left. \mspace{25mu}{{if}\mspace{14mu}({PWLD})2} \right)=={NO\_ INDICATION}}\;\&\&\mspace{11mu}{{{PWLD}(2)}=={POSSIBLY\_ LIFTED}}} \right) \\{\mspace{25mu}\{} \\{\mspace{50mu}{{if}{~~}\left( {{{P_{\tau}(2)}==1}\;\&\&\mspace{11mu}{{\theta_{{rr}\text{-}{whl}}(1)} \geq {{p\_ LFT}{\_ NDW}{\_ WDA}{\_ TH}}}} \right.}} \\{\mspace{50mu}\left. ||{{{P_{\tau}(2)}==2}\;\&\&\mspace{11mu}{{\theta_{{rr}\text{-}{whl}}(1)} \geq {{p\_ LFT}{\_ DW}{\_ WDA}{\_ TH}}}} \right.} \\{\mspace{50mu}\left. ||{{{P_{\tau}(2)}==1}\;\&\&\mspace{11mu}{{\theta_{{rr}\text{-}{whl}}(1)} \geq {{p\_ LFT}{\_ DW}{\_ WDA}{\_ TH}}}} \right.} \\{\mspace{50mu}{\&\&\;\left( \left. {{DRIVE\_ MODE}=={FRONT}}||{{DRIVE\_ MODE}=={FOUR}} \right.|| \right.}} \\\left. \mspace{149mu}{{DRIVE\_ MODE}=={TOD}} \right) \\\left. \mspace{76mu} \right) \\{\mspace{50mu}\left\{ {{{{PWLD}(2)} = {ABSOLUTELY\_ LIFT}};} \right\}} \\{\mspace{50mu}{{if}\mspace{14mu}\left( {{s_{p}(2)} \leq {{- {p\_ LFT}}{\_ SP}{\_ MIN}{\_ TH}}} \right)}} \\{\mspace{50mu}\left\{ {{{{PWLD}(2)} = {POSSIBLY\_ GROUNDED}};} \right\}} \\\left. \mspace{25mu} \right\} \\\}\end{matrix} & (52)\end{matrix}$

Notice that the drive mode is checked in order to distinguish betweendriven wheel engine braking and non-driven wheel braking. If the slippower is negative enough, i.e., the slip ratio has rapid convergentrate, then possibly grounded wheel condition is identified.

A detailed logic can be summarized as the following for the left loadedwheel case:

if θ_(xr) ≦ 0 {  if (PWLD(1) == NO_INDICATION & &PWLD(1) == POSSIBLY_LIFTED)  {   if ( P_(τ)(1) == 1 & & θ_(rr-whl)(0) ≦−p_LFT_NDW_WDA_TH   || P_(τ)(1) == 2 & & θ_(rr-whl)(0) ≦−p_LFT_DW_WDA_TH   || (P_(τ)(1) == 1 & & θ_(rr-whl)(0) ≦−p_LFT_DW_WDA_TH   & & (DRIVE_MODE == FRONT ∥ DRIVE_MODE == FOUR ||    DRIVE_MODE == TOD) )    )   { PWLD(1) = ABSOLUTELY_LIFTED;  }   if(s_(p)(1) ≦ −p_LFT_SP_MIN_TH )   { PWLD(1) = POSSIBLY_GROUNDED;  }  } if (PWLD(3) == NO_INDICATION & &PWLD(3) ==  POSSIBLY_LIFTED)  {   if(P_(τ)(3) == 1 & & θ_(rr-whl)(1) ≦ p_LFT_NDW_WDA_TH   || P_(τ)(3) == 2 && θ_(rr-whl)(1) ≦ p_LFT_DW_WDA_TH   || P_(τ)(3) == 1 & & θ_(rr-whl)(1) ≦p_LFT_DW_WDA_TH   & & (DRIVE_MODE == FRONT || DRIVE_MODE == FOUR ||    DRIVE_MODE == TOD)    )   { PWLD(3) = ABSOLUTELY_LIFT;  }   if(s_(p)(3) ≦ − p_LFT_SP_MIN_TH )   { PWLD(3) = POSSIBLY_GROUNDED;  }  } }

Referring now to FIG. 6, a method for controlling an automotive vehicleas described above is now summarized. In step 70, the vehicle constantsare determined. As described above, various vehicle constants are usedin the present embodiment. The vehicle constants are determined duringvehicle testing and vary with different suspensions and vehicleconfigurations. Such vehicle constants include suspension resultant rollstiffness K_(roll), roll damping rates D_(roll), the height of thecenter of gravity of the vehicle, the masses of the vehicle includingthe inertial masses which include the roll moments of inertia of thefront and rear wheel tire assemblies around the contact patches of theouter tires, and the total masses of the front and rearwheels/tires/suspension assemblies. In step 72 the various sensors areread. The various sensors may include sensors in FIG. 2. In steps 74-82a first through fifth roll conditions are determined. The conditions mayinclude a relative roll angle and a wheel departure angle calculatedfrom a roll rate sensor and a lateral acceleration sensor, a rollingradius-based wheel departure angle, normal loading at each wheel, anactual road torque and a wheel longitudinal slip. At least threedeterminations are desirable. However, for a more robust system all fiveroll conditions may be determined.

In step 84 wheel lift in response to the roll conditions are determined.In step 86 the rollover control system may be activated to countervehicular rolling motion in response to the wheel lift signal. Ofcourse, as described below actuation may be based on a roll angle whilethe wheel lift detection may be used to adjust various parameters suchas relative roll angle or the road bank angle.

What has been described above are several different ways in which todetermine wheel lift passively.

Active Wheel Lift Using Change of Torque

Both passive and active wheel lift detection may be used in a rollovercontrol system or other safety system.

From FIG. 2A above, the command controller 56 may include a torquecontroller 57 that is used to control the torque of the wheels 12A, 12B,13A, 13B. Torque controller 57 may act in conjunction with theelectronic engine controller, a driveline engagement mechanism orbraking system, or a combination of these to control the torque at oneor all of the wheels 12A, 12B, 13A, 13B. Torque controller 57 and rollcontroller 18 may be coupled to wheel speed sensors 20 located at eachof the wheels. Wheel speed sensors 20 provide roll control system 26with a signal indicative of the speed of the individual wheel to whichit is attached. Various types of wheel speed sensors includingtoothed-wheel type systems would be evident to those skilled in the art.

In the following active wheel lift example, the application of brakepressure is used to provide the change in torque. However, other methodssuch as applying engine torque may also be used to change the amount oftorque at a wheel. Further references to the application of torque to awheel may include hydraulic or electric brake torque, changes in enginetorque or engagement of driveline torque through the use of anelectronically controlled transfer case, differential, transmission orclutch. The present embodiment may also be used to determine if a sensorhas failed in the sensor system 16. That is, if roll is suspected by aparticular sensor, but all other conditions or sensors indicateotherwise, the sensor may be operating improperly. Also, although speedis used, wheel acceleration may also be used in place of speed as wouldbe evident to those skilled in the art.

Referring now to FIG. 7, the active wheel lift detector 60 is used toperform the following method and generate an active wheel lift signal.In step 130, if a roll sensor failure is suspected or in step 132 ifwheel lift is suspected by the roll control system, block 134 initiatesthe wheel lift determination process. In step 136, torque is applied tothe wheel suspected of lifting and the wheel speed at the suspectedwheel is stored. In step 138, the torque is increased by applying a testpulse of torque to the suspected wheel. Torque is applied until a torquethreshold (Torque_Max) is achieved. In step 140, if the torque isgreater than the Torque_Max, the torque is held constant in step 142. Instep 144, if the time as counted by the Build_Counter is greater than apredetermined time, step 146 is executed in which the torque is releasedand the wheel speed at the initiation of the release of torque isstored. In step 144, if the counter is not greater than thepredetermined hold time, the counter is incremented in step 148. Afterstep 148 the change in wheel speed is compared to a predetermined changein wheel speed. If the wheel speed change is not greater than apredetermined speed in step 150, steps 138-144 are again executed. Ifthe wheel speed change is greater than a predetermined speed, thisindicates a lifted wheel. In this case, step 152 is executed in which awheel lift status flag is set. After step 152, step 154 is executed inwhich the build counter is reset.

Referring back to step 140, if the torque is not greater than the torquethreshold then step 150 is executed.

Referring back to step 146, after the wheel speed is recorded after thetorque release, step 156 is executed. In step 156 torque is released.After step 156, step 158 is implemented in which the wheel speed changeis compared to a reacceleration threshold. The reacceleration thresholdis a predetermined value that corresponds to a wheel speed change thatshould be achieved should wheel contact be reestablished. The wheelspeed change is determined from the time that the torque was released.If the wheel speed change is greater than a reacceleration threshold orif the wheel lift status from step 152 is zero, wheel contact isassumed. In such a case the traction level may be calculated in step160. If the wheel speed does not increase over the reaccelerationthreshold, then the wheel lift status is confirmed beginning with step170.

Referring back to step 158, if the wheel speed is less than thereacceleration threshold, step 162 compares the Dump_Counter to apredetermined dump time. If the predetermined dump time is greater thanthe Dump_Counter, then the Dump_Counter is incremented in step 164 andsteps 156 and 158 are again executed. If the Dump_Counter is greaterthan the predetermined dump time, then the wheel lift status flag is setin step 166 and the Dump_Counter is reset in step 168. After step 168,the process is reinitiated and returns to step 136.

Returning back to step 160, the traction level is calculated in step160. After step 160, the plausibility of a sensor failure is determined.If, for example, the process was initiated based on the suspicion of asensor failure from block 130 above and no wheel lift was detected, asensor failure is indicated in step 172. For either result, if a sensorfailure is indicated by block 170 or not, the build counter andDump_Counter are cleared in block 174 and the wheel lift status iscleared in block 176. The end of the routine occurs in block 178.

Thus, as can be seen, the application of torque can be used to firstdetermine whether a suspected wheel has lifted from the pavement. Forconfirmation, the removal of the torque and the resulting wheel speedchange may be used to confirm the initial finding. Advantageously, thesystem may be implemented in a dynamic stability system of an automotivevehicle without adding further sensors. If rollover is detected, thenthe rollover can be corrected by applying the brakes or generating asteering correction.

Referring now to FIG. 8A, various lines 190, 192, 194 are illustratedduring the build time to illustrate the variation in pressure of thebraking system due to wear and other effects of the brakes. Lines 190,192 194 have little effect on the overall operation of the system. Thus,the thresholds and parameters are selected so that the system is robustto wear and system variation. The maximum pressure p_(max) is reachedand maintained for a hold time (such as set forth in step 42 above)until it is released.

Referring now to FIG. 8B, a plot of wheel speed corresponding to thevarious times is illustrated. As shown, the wheel speed of a loadedwheel is illustrated by line 196, which is higher than the wheel speedof a lifted wheel illustrated by line 198.

Passive Wheel Lift Using Torques

Referring now to FIG. 9, a passive method similar in theory to theactive method is hereinafter described. That is, rather than applying achanging torque to the wheel, an operating input torque to the wheel maybe used. This passive determination may be used in the method of FIG. 6described above. Thus, the operating input torque to the wheel is anunmodified wheel torque from those of the normal operating conditions incontrast to that described in the parent application U.S. Pat. No.6,356,188, which is incorporated by reference herein. Consequently, thepassive system described below can accommodate the type of normaloperating wheel torque, from low or near zero, to negative (braking) orpositive (accelerating). It should be noted that each wheel may besubject to this method.

In step 210, the various sensors in vehicle conditions are read. Thefollowing process is performed for each of the wheels. In step 220, thevarious inputs to the method are obtained and calculated. The inputtorque may be measured by a separate sensor or may be determined usingthe engine torque. The operating input torque to the wheel is a functionof the engine speed, and the distribution of the engine torque to thewheels through a torque transferring system such as a differential anddriveline. Thus, the operating input torque may be determined withoutbeing modified. In contrast to an active system, the active system musthave and generate a change in torque. The slip ratio of each wheel isalso determined. The wheel slip ratio is determined by the difference ofthe wheel speed minus the velocity of the corner divided by the vehiclespeed at the corner. Thus, the wheel slip ratio is a unitless ratio. Thevelocity at each corner of the vehicle may be determined from the wheelspeed sensors described above or may be a function of the yaw rate toaccount for the turning of the vehicle. Thus, the yawing of the vehicleand the speed at the vehicle may be used to determine the vehiclevelocity at the corner of the vehicle.

In step 220, the wheel acceleration and the slip rate of the vehicle mayalso be determined. The vehicle slip rate is the change in the slipratio described above. That is, the slip ratio derivative is used todetermine the slip rate. However, the velocity at each corner of thevehicle multiplied by the derivative of the slip ratio may also be usedas the slip rate. It has been found in practice that this method fordetermining the slip rate results in a cleaner signal, which isadvantageous in signal processing.

In step 222, the magnitude and sign (or direction) of the input torqueis determined. In step 224, if a large magnitude of input torque isprovided (not near zero) step 224 is executed. Step 224 checks the wheelslip ratio. The sign or relative direction of wheel slip ratio and themagnitude of the wheel slip ratio is compared to thresholds. If thewheel slip ratio is greater than a predetermined magnitude and it hasthe same sign as the input torque, step 226 is executed.

In step 226, the wheel response is determined. The wheel response may bedetermined using the wheel acceleration, the wheel slip rate, or both.The wheel response and the wheel slip ratio are compared to a threshold.The threshold may be a function of the input torque. The terms divergentand convergent are also used. Divergent means that the values aretrending away from zero, while convergent means the values are trendingtoward zero. In step 226, if the wheel acceleration and slip rate areboth divergent and above predetermined corresponding thresholds, step228 is executed in which a possibly lifted counter is incremented. Ifthis condition holds for a number of cycles, step 230 generates a liftedwheel signal indicative that the wheel has lifted.

In step 230, other vehicle inertial information may be used to confirmthe identity and possibility that the wheel is lifted.

Referring back to step 226, if the wheel acceleration and/or the wheelslip rate is divergent but below a predetermined threshold, step 232provides no indication to the system. That is, not enough informationhas been provided.

In step 226, if the wheel acceleration and the wheel slip rate isconvergent, step 234 is executed. In step 234 a possibly grounded signalis generated and a grounded counter is incremented. In step 236, if theabove condition persists for a predetermined number of cycles, a wheellifted signal is generated for the wheel.

Referring back to step 224, if the wheel slip is about zero, step 238 isexecuted. In step 238, if the wheel response is below the threshold,step 234 is executed as described above. The thresholds may be the sameas those described above or may be changed due to the change of torque.The threshold may also be constant numerical values. If in step 238 thewheel responses are above the thresholds, no information is provided.

Referring back to step 224, if the wheel slip ratio has a largemagnitude but has a sign opposite to the input torque, no information isgenerated in step 242.

Referring back to step 222, if a small input torque near zero isgenerated (the absolute value of the input torque is less than apredetermined input torque) the wheel state is checked in step 244. Instep 244 the magnitude of the wheel slip is determined. If the wheelslip is above a predetermined threshold, the response of the wheel ischecked in step 246. For small torque cases, the wheel response is notlikely to be divergent. However, in this case, lack of convergence maybe used to indicate that the wheel is not grounded. Note that if thewheel does meet the divergence criteria, it also meets thenon-convergent criteria. Thus, if the wheel state is convergent in step246, step 234 is executed. In step 246, if the wheel response isnon-convergent, that is, that significant slip is present and the wheeldoes not have significant acceleration of opposite sign compared to theslip ratio, step 228 is executed. If a smaller input torque and a smallwheel slip is present from step 224, step 248 indicates no information.

The no information blocks 232, 240, 242, and 248 are all used to provideno indication of wheel lift. This is because insufficient evidence orconflicting evidence is present.

One advantage of this passive wheel lift determination is that thecomputations may be run at all times and is generally independent of theinertial state information.

Arbitration Between Active and Passive Wheel Lift

The passive wheel lift detection strategy (PWLD) checks all theavailable motion variables at each time instant to determine if asuspicious wheel is lifted. The advantage of PWLD over AWLD is that theformer could send an indication at each time instant, and the latterneeds to wait a certain period of time before sending out an indication.Another advantage is that during driver braking, PWLD can be usedeffectively to identify wheel lifting. However PWLD, in some cases,suffers a lack of information to determine the wheel lifting status ifthe wheel slip is not disturbed enough and sufficient torque is notpresent.

Therefore, it is desirable to integrate active and passive wheel lifttogether so as to conduct a reliable wheel lift determination. The finalwheel lift status may be used for activating the roll stability controlsystem or updating various parameters.

The passive wheel lift detection (PWLD) system generates the wheellifting status S_(wld-passive)(i) for the ith wheel, which could be anyof the following five statuses. The following statuses are set forth inan order from high to low. The statuses may actually be implemented as anumber in the logic of the control scheme. For example “4” may representabsolutely grounded while “0” represents no indication.

If the ith wheel is absolutely grounded, thenS _(wld-passive)(i)=ABSOLUTELY_GROUNDED

If the ith wheel is in the edge of grounding,S _(wld-passive)(i)=POSSIBLY_GROUNDED

If the ith wheel is absolutely lifted, thenS _(wld-passive)(i)=ABSOLUTELY_LIFTED

If the ith wheel is in the edge of liftingS _(wld-passive)(i)=POSSIBLY_LIFTED

If the ith wheel's status cannot be confirmed, thenS _(wld-passive)(i)=NO_INDICATION

As mentioned above there are numerous methods for determining passivewheel lift detection for setting S_(wld-passive)(i).

Active Wheel lift detection, as described above is intended to be anindependent means of determining whether a wheel is lifted or not. Byindependent, it is meant that the detection method does not rely on thesignals used to detect the roll state of the vehicle (i.e., roll rateand angle, lateral acceleration, steering wheel angle, vehicle speed,steering wheel angle). Basically, the operation of the algorithm isbroken into a Build Cycle, in which brake pressure is applied to thewheel, and a Release Cycle, in which brake pressure is removed from thewheel. In the Build and Release Cycles, the slip ratio and rate of wheelspeed change is compared to a physical model of a lifted and a groundedwheel, in order to determine the Lift State.

The intent of the Build cycle is to apply brake pressure to the wheel inorder to (i) generate negative slip on the wheel. Typically slip ratiosless than (more negative than) −15 to −20% are required to assess if awheel is lifted. Furthermore, slip ratios of this magnitude are requiredto assess the Lift State of the wheel in the Release Cycle; (ii) Examinethe rate of wheel speed change as a function of brake pressure andengine torque during the build cycle.

The intent of the Release cycle is to remove brake pressure on the wheel(Upon Entering Release Initial, the requested pressure on the wheel isset to zero) and (i) examine the rate of wheel speed change as afunction of residual brake pressure and engine torque; (ii) Examine thechange in slip ratio as a function of the release counters (i.e., timein release).

The active wheel lift detection system generated the wheel liftingstatus S_(wld-active)(i) for the ith wheel.

A simple arbitration between S_(wld-passive)(i) and S_(wld-active)(i) toprovide a final wheel lifting status S_(wld)(i) can be expressed as inthe following

for (i = 0; i ≦ 3; i + +) {  if(S_(wld-active)(i) ==ABSOLUTELY_GROUNDED)   S_(wld)(i) = ABSOLUTELY_GROUNDED;  elseif(S_(wld-active)(i) == ABSOLUTELY_LIFTED)   S_(wld)(i) =ABSOLUTELY_LIFTED;  else if(S_(wld-passive)(i) == ABSOLUTELY_GROUNDED)  S_(wld)(i) = ABSOLUTELY_GROUNDED;  else if(S_(wld-passive)(i) ==ABSOLUTELY_LIFTED)   S_(wld)(i) = ABSOLUTELY_LIFTED;  elseif(S_(wld-active)(i) == POSSIBLY_GROUNDED)   S_(wld)(i) =POSSIBLY_GROUNDED;  else if(S_(wld-active)(i) == POSSIBLY_LIFTED)    S_(wld)(i) = POSSIBLY_LIFTED;  else if (S_(wld-passive)(i) ==POSSIBLY_GROUNDED)   S_(wld)(i) = POSSIBLY_GROUNDED;  elseif(S_(wld-passive)(i) == POSSIBLY_LIFTED)   S_(wld)(i) =POSSIBLY_LIFTED;  else   S_(wld)(i) = NO_INDICATION; }

Although the above simple integration scheme provides an envelope forboth active and passive wheel lifting status, no conflict resolution isprovided. In the logic above, i refers to the wheel number. The frontleft wheel is 0, the front right wheel is 1, the rear left wheel is 2,and the rear right wheel is 3. Thus, wheels 0 and 2 are on the same side(left in this case) of the vehicle while wheels 1 and 3 are on the sameside (right in this case) of the vehicle. In the above logic, if theactive wheel lift signal is absolutely grounded, the final wheel liftstatus is set to be absolutely grounded. If the above is not true andthe active wheel lift status is absolutely lifted the final wheel liftstatus is set to absolutely lifted. If the above is not true and thepassive wheel lift status is absolutely grounded, then the final wheellift status is absolutely grounded. If the above is not true and thepassive wheel lift status is absolutely lifted then the final wheel liftstatus is set to be absolutely lifted. If the active wheel lift statusis possibly grounded and the above is not true, then the final wheellift status is set to be possibly grounded. If the above is not true andthe active wheel lift status is possibly lifted then the final wheellift status is set to possibly lifted. If the above is not true and thepassive wheel lift status is possibly grounded, then the final wheellift status is said to be possibly grounded. If the above is not trueand the passive wheel lift status is possibly lifted, then the finalwheel lift status is set to be possibly lifted. If any of the above arenot true then the final wheel lift status is set to no indication.

For example, such an integration does not distinguish between a conflictbetween S_(wld-passive)(i) and S_(wld-active)(i) The following conflictremoving logic (CRL) which is part of the logic programmed intointegrated wheel lift detector 62 sets the final wheel lifting statusS_(wld)(i) to NO_INDICATION instead of sending out a potentially wrongstatus

for (i = 0; i ≦ 3; i + +) {  if(  (S_(wld-active)(i) ≦ POSSIBLY_GROUNDED& &     S_(wld-passive)(i) ≧ POSSIBLY_LIFTED)    || (S_(wld-active)(i) ≧POSSIBLY_LIFTED & &     S_(wld-passive)(i) ≦ POSSIBLY_GROUNDED)   )   S_(wld)(i) = NO_INDICATION; }

In the above logic, when the active wheel lift status is less than orequal to possibly grounded and the passive wheel lift is greater than orequal to possibly lifted for the same wheel, or the active wheel lift isgreater than or equal to possibly lifted and the passive wheel liftsignal is less than or equal to possibly grounded then no indication isprovided. As can be seen, this logic provides a conflict check betweenthe passive wheel lift signal and the active wheel lift signal for eachof the wheels.

Due to different suspension systems, some vehicle may have earlier frontwheel lifting and a delayed rear wheel lifting; others may have rearwheel lifting first and then the front wheel lifting. In this case aconsistence check for the final wheel lift status can be conducted as inthe following CONSISTENCY CHECK LOGIC (CCL). If a vehicle has earlierfront wheel lifting

if(  S_(wld)(0) ≦ POSSIBLY_GROUNDED   & &S_(wld)(2) ≧ POSSIBLY_LIFTED  ){    S_(wld)(0) = NO_INDICATION;     S_(wld)(2) = NO_INDICATION; } if( S_(wld)(1) ≦ POSSIBLY_GROUNDED   & &S_(wld)(3) ≧ POSSIBLY_LIFTED  )   S_(wld)(1) = NO_INDICATION;     S_(wld)(3) = NO_INDICATION; }

In the above logic, the final wheel lift status for both sides of thevehicle are checked. On the left side of the vehicle if the wheel liftstatus of the front wheel is less than or equal to possibly grounded andthe rear wheel is greater than or equal to possibly lifted, both of thefinal wheel lift statuses for both the front and the rear wheels of theleft side of the vehicle are set to no indication. The same is true forthe right side of the vehicle.

If a vehicle has earlier rear wheel lifting

if(  S_(wld)(2) ≦ POSSIBLY_GROUNDED   & &S_(wld)(0) ≧ POSSIBLY_LIFTED  ){    S_(wld)(0) = NO_INDICATION;     S_(wld)(2) = NO_INDICATION; } if( S_(wld)(3) ≦ POSSIBLY_GROUNDED   & &S_(wld)(1) ≧ POSSIBLY_LIFTED  )   S_(wld)(1) = NO_INDICATION;     S_(wld)(3) = NO_INDICATION; }

Both the right side of the vehicle and the left side of the vehicle arechecked in the above logic. If the final wheel lift status for the rearwheel is less than or equal to possibly grounded and the front leftwheel is greater than or equal to possibly lifted, then both of thefront and rear wheel final wheel lift statuses are set to no indication.The same is true for the right side of the vehicle as well.

If the vehicle relative roll angle is very small and the roll ratesignal tries to decrease the relative roll angle, then anotherconsistency check logic (CCL) can be conducted. If the vehicle isturning left

if(  θ_(xr) ≧ 0 & &θ_(xr) ≦ Θ & &ω_(x) ≦ 0 ) {  if(S_(wld)(0) ≧POSSIBLY_LIFTED)  {   S_(wld)(0) = NO_INDICATION;  }  if(S_(wld)(2) ≧POSSIBLY_LIFTED)  {   S_(wld)(2) = NO_INDICATION;  } }

In the above logic, if the roll angle is greater than 0 and the rollangle is less than or equal to a threshold, indicative that the rollangle is small, and the roll rate is less than or equal to 0 and thefinal wheel lift status of the front left wheel is greater than or equalto possibly lifted, then no indication is provided. Likewise, if thefinal wheel lift status of the left rear wheel is greater than or equalto possibly lifted then no indication is provided. As can be seen by thelogic immediately below, the relative roll angle, the threshold and theroll rate may be used to detect a consistency in the right side of thevehicle. That is, if the relative roll angle θ_(xr) is less than orequal to 0 and the relative roll angle is greater than or equal to thenegative relative roll angle threshold and the roll rate is greater thanor equal to 0, and if the final wheel lift status of the front rightwheel greater than or equal to possibly lifted, no indication isprovided. The same check is performed for the rear wheel.

If the vehicle is turning right

if( θ_(xr) ≦ 0 & &θ_(xr) ≧ −Θ& &w_(x) ≧ 0 ) {  if(S_(wld)(1) ≧POSSIBLY_LIFTED)  {   S_(wld)(1) = NO_INDICATION;  }  if(S_(wld)(3) ≧POSSIBLY_LIFTED)  {     S_(wld)(3) = NO_INDICATION;  } }

Considering the roll stability control system applies braking pressureto the front wheels during the initial stage of pressure build-up,braking pressure for active wheel lift detection on the other wheel thatshares a brake circuit with the RSC control wheel is terminated so as toguarantee all the brake fluid in the brake circuit will be used to buildcontrol pressure. Hence if the vehicle has a front-rear split brakingsystem, the following pressure inhibit logic (PIL) will be used to turnoff active wheel lift detection (AWLD)

if(P_(RSC)(0) ≦ P_(est)(0) + γ) {  Turn off AWLD at wheel 1;  S_(wld)(1)= S_(wld-passive)(1) } if(P_(RSC) ^((1) ≦ P) _(est)(1) + γ) {  Turn offAWLD at wheel 0;  S_(wld)(0) = S_(wld-passive)(0) }where P_(RSC)(i) is the rollover stability control system requestbraking pressure at front wheels, P_(est)(i) is the estimated caliperpressure, and

is a pressure offset. As can been seen by the above logic, if either ofthe pressure requested by the front wheels is less than or equal to anestimated caliper pressure plus an offset, the final wheel status ofeither of the front wheels is then set to the passive wheel status.Therefore, the active wheel check for the particular wheel is disabled.

If the vehicle has a diagonal split braking system, the followingpressure inhibit logic (PIL) will be used to turn off active wheel liftdetection (AWLD).

if(P_(RSC)(0) ≦ P_(est)(0) + γ) {  Turn off AWLD at wheel 1;  S_(wld)(1)= S_(wld-passive)(1) } if(P_(RSC)(1) ≦ P_(est)(1) + γ) {  Turn off AWLDat wheel 0;  S_(wld)(0) = S_(wld-passive)(0) }

Considering that during driver braking, the torque disturbance is enoughto initiate a solid PWLD result, the following driver braking detectionintegration logic (DBDIL) is conducted

if(DRIVER_BRAKING_FLAG == 1   & &P_(driver) ≧ Ψ) {  Turn off AWLD atwheel i;  S_(wld)(i) = S_(wld-passive)(i) }where Ψ is a threshold for driver braking pressure P_(driver).

Thus, as can be seen by the above logic, if the driver or vehicleoperator applies the brakes a braking flag will be generated. If thebrake pressure requested by the driver is above a threshold then activewheel lift is disabled for the wheel. That is, the final wheel status isset to the passive wheel status.

Considering that during a large driving torque application (for example,wide open throttle case), there are enough wheel torque disturbance toinitiate a solid PWLD result, the following open throttle detectionintegration logic (OTDIL)

if(OPEN_THROTTLE_FLAG == 1   & &T_(driving) ^((i) ≧ Γ)) {  Turn off AWLDat wheel i;  S_(wld)(i) = S_(wld-passive)(i) }where τ_(driving)(i) is the positive driving torque applied to the ithwheel due to engine torque and Γ is the threshold for τ_(driving)(i).

As the above logic shows, when the driving torque for a particular wheeldue to engine is compared to a threshold, which indicates a throttlestatus such as wide open throttle, the active wheel lift detection isdisabled. That is, the final wheel lift status Swld is set to thepassive wheel lift status.

Angle Corrections from Wheel Lift/Grounded Determination

Referring now to FIG. 10, the relationship of the various angles of thevehicle 10 relative to the road surface 11 is illustrated. In thefollowing a reference road bank angle θ_(bank) is shown relative to thevehicle 10 on a road surface. The vehicle has a vehicle body 10 a andwheel axle 10 b. The wheel departure angle θ_(wda) is the angle betweenthe wheel axle and the road. The relative roll angle θ_(xr) is the anglebetween the wheel axle 10 b and the body 10 a. The global roll angleθ_(x) is the angle between the horizontal plane (e.g., at sea level) andthe vehicle body 10 a.

Another angle of importance is the linear bank angle. The linear bankangle is a bank angle that is calculated more frequently (perhaps inevery loop) by subtracting the relative roll angle generated from alinear roll dynamics of a vehicle (see U.S. Pat. No. 6,556,908 which isincorporated by reference herein), from the calculated global roll angle(as the one in U.S. application Ser. No. 09/789,656, which isincorporated by reference herein). If all things were slowly changingwithout drifts, errors or the like, the linear bank angle and referenceroad bank angle terms would be equivalent.

Referring now to FIG. 11, controller 26 is illustrated in furtherdetail. The controller 26 receives the various sensor signals 20, 28-39.From the various sensor signals wheel lift detection may be determined.The modules described below (and above) may be implemented in hardwareor software in a general purpose computer (microprocessor). From thewheel lift detection module 52, a determination of whether each wheel isabsolutely grounded, possibly grounded, possibly lifted, or absolutelylifted may be determined, as described above. Transition detectionmodule 252 is used to detect when the vehicle is experiencing aggressivemaneuver during a transition turn from the left to right or right toleft. The sensors may also be used to determine a relative roll angle inrelative roll angle module 54. Relative roll angle may be determined inmany ways. One way is to use the roll acceleration module 258 inconjunction with the lateral acceleration sensor (see U.S. Pat. No.6,556,908 incorporated by reference herein) for detail. As describedabove, the relative roll angle may be determined from the rollconditions described above.

The various sensor signals may also be used to determine a relativepitch angle in relative pitch angle module 256 and roll acceleration inroll acceleration module 258. The outputs of the wheel lift detectionmodule 50, the transition detection module 52, and the relative rollangle module 54 are used to determine a wheel departure angle in wheeldeparture angle module 260. Various sensor signals and the relativepitch angle in relative pitch angle module 256 are used to determine arelative velocity total in module 262. The road reference bank anglestep 264 determines the bank angle. The relative pitch angle, the rollacceleration, and various other sensor signals as described below areused to determine the road reference bank angle. Other inputs mayinclude a roll stability control event (RSC) and/or the presence of arecent yaw stability control event (WLDFlag).

The global roll angle of the vehicle is determined in global roll anglemodule 266. The relative roll angle, the wheel departure angle, and theroll velocity total blocks are all inputs to the global roll anglemodule 266. The global roll angle block determines the global roll angleex. An output module 68 receives the global roll angle module 266 andthe road reference bank angle from the road reference bank angle module264. A roll signal for control, which will be directly used ingenerating control command from the feedback control law, is developedin roll signal module 270. The roll signal for control is illustrated asarrow 272. A sensitizing and desensitizing module 74 may also beincluded in the output module 68 to adjust the roll signal for control.

In the reference road bank angle module 264, the reference bank angleestimate is calculated. The objective of the reference bank estimate isto track the true road bank angle experienced during driving in bothstable and highly dynamic situations. Most importantly, when compared tothe global roll estimate, it is intended to capture the occurrence andphysical magnitude of a divergent roll condition (two wheel lift) shouldit occur. This signal is intended to be used as a comparator against theglobal roll estimate for calculating the error signal of the rollcontroller 26.

The roll signal for control is calculated as the (θ_(x)−θ_(refbank)),i.e., the subtraction of the reference bank angle from the global rollangle.

As mentioned above various errors not limited to integration,calculation and drift may enter into the various signals at varioustimes. Thus, in certain situations the wheel departure angle or thereference bank angle may not be accurate. The following descriptiondescribes how these values can be updated in response to wheellift/wheel grounded values.

As described above, wheel lift detection includes both detecting thatthe wheels are grounded and that the wheels are lifted. These conditionsare relatively certain and thus may be used to update certain calculatedvalues such as the reference roll angle and the wheel departure angle.

Referring now to FIG. 12, a high level flow chart illustrating thecondition detection and the resulting actions according to thisembodiment of the present invention is illustrated. In step 300 varioussensors described above are read. In step 302 various method selectionsbased upon the particular drive train are determined. For example, themethod selection may adjust the various factors based upon the presenceand condition of the center differential. This step will be furtherdescribed in FIG. 13.

In step 304, passive wheel lifting/grounding detection is determined.Thereafter, in step 306, a final lifting/grounding condition arbitrationis performed.

Referring back to step 302, a parallel process to that of step 304 isdescribed. In step 308 it is determined whether or not active detectionis required. If active detection is not required step 306 is performed.If after detection is required, step 310 performs active wheellift/grounding detection. Thereafter, step 306 arbitrates between thelifting and grounding conditions as described above. The arbitratedcondition for each of the wheels of the vehicle is determined. Afterstep 306, the resulting actions from the wheel lifting/groundingconditions are determined. Step 304 is further described in FIG. 14.Step 310 is further described in FIG. 15 and step 312 is furtherdescribed in FIG. 16.

As shown in step 268 of FIG. 11, the roll signal for control isultimately determined. The roll signal for control is a function of theglobal roll angle and the reference roll angle. The reference bank anglemay also be adjusted in response to the wheel departure angle and therelative roll angle generated from a linear roll dynamics model as willbe further described below.

Referring now to FIG. 13, step 320 describes whether a centerdifferential is engaged. If the center differential is engaged in step320, step 322 determines whether or not this engagement is feasible orrequired. If the disengagement is not feasible or required then step 328selects an averaging method for the two sides of the vehicle.

When the vehicle is in 4×4 mode, the front and rear axles are coupledthrough the driveshaft. This drivetrain coupling results in an unknownfront/rear torque split and causes transient oscillations of the wheels.These factors prevent an accurate evaluation of lift for each wheel end,but lift can still be evaluated by treating the wheels on each side ofthe vehicle as a two-wheel system. By considering all torques on thetwo-wheel system and looking at the overall system response, a methodanalogous to the individual wheel method can be used to detect lift.

For each side of the vehicle, the two-wheel system response isdetermined by averaging the responses of the front and rear wheels onthat side. The key change for 4×4 wheel lift detection is that theaverage wheel speeds and slip values (front averaged with rear for eachside of the vehicle) are used instead of values for each individualwheel. The lift is evaluated for each side of the vehicle instead ofevaluating each wheel. By the above a robust identification location oftwo wheel lift is determined. Single wheel life may be identified onlywhen there is a sufficiently low amount of loading on the second wheel.

In step 322 if the disengagement is feasible and required, step 324disengages the center differential. Thereafter, step 326 is performed.Step 326 is also performed if the center differential is not engaged instep 320. An individual method is used in step 326. That is, individualmethod selects the individual wheels of the front or rear of thevehicle.

Referring now to FIG. 14, step 304 above is described in further detail.The grounding/lifting conditions described below may be determinedwithin the wheel lift detection module. In step 330, the groundingcondition is screened. If the grounding condition is determined in step330, the passive wheel grounding condition detector is set. That is, thepassive wheel lift being absolutely grounded is determined. In step 334,the passive detection arbitration logic receives the absolutely groundedcondition for the wheel. In parallel, the lifting condition is screenedin step 336. In step 336, if lifting condition is passively detected instep 338 the output is provided to passive detection arbitration logic334. In steps 330 and 336, if an absolutely grounded or absolutelylifting condition is not determined, the AND block of step 340 is usedto form a no indication detector in step 342. After step 342 the passivedetection arbitration logic 334 provides a final passive detectionsignal. The output of the passive detection arbitration logic 334 is anabsolutely lifted condition, possibly lifted condition, an absolutelygrounded condition, a possibly grounded condition, or a no indicationdetector. The no indication detector is generated when the conditionsare not absolutely or possibly true. That is, the conditions other thanthe aforementioned four conditions will be deemed as no indication.

Referring now to FIG. 15, step 350 generates an active torque control.Steps 352, 354 and 356 corresponded to the logic described above. Thatis, step 352 determines active wheel grounding in response to the activetorque provided in step 350. In step 354 active wheel lift is detectedand in step 356 a no indication detector is provided. In step 358, theno indication detector is conducted when the conditions are notabsolutely or possibly true. The detection arbitration logic in step 358thus provides an absolutely grounded condition, an absolutely liftedcondition, possibly grounded condition, possibly lifted condition or ano indication for each of the wheels.

Referring now to FIG. 16, step 312 is illustrated in further detail. Instep 312, the terminology illustrated on the figures is as follows: FIis the front inside wheel of the turn, RI is the rear inside wheel ofthe turn, AG is an absolutely grounded flag, NI indicates no indication,AL indicates absolutely lifted, and WDA is the wheel departure angle.The front inside wheel and the rear inside wheel refer to the positionof the wheels while making a turn. Thus, in a left hand turn the frontinside wheel would be the left front wheel whereas the left rear wheelwould be the rear inside wheel. In a right hand turn the front insidewheel is the front right wheel whereas the rear inside wheel is the rearright wheel.

In steps 360 and 362 the front inside wheel and the rear inside wheelare determined whether or not they are absolutely grounded. If one orthe other is absolutely grounded step 364 is executed. Thus, if eitherone of the front inside wheel or the rear inside wheel is absolutelygrounded, step 368 is executed. In step 368 the reference bank angle isramped down toward the linear bank angle. Although one single adjustmentcould be made, in a control system it may be desirable to graduallyincrement the reference bank angle to the linear bank angle. This logicis true because the linear bank angle which is calculated more oftenthan the reference bank angle is a more accurate representation of theroad bank than the reference bank angle when at least one of the frontor rear inside wheels is absolutely grounded. After step 368, step 314of FIG. 12 is executed. In step 370 it is determined whether the frontinside wheel is absolutely grounded or the front outside wheel isoutside is less than or equal to a no indication status. Less than orequal to no indication status indicates absolutely or possibly grounded.In step 372 it is determined the right inside wheel is absolutelygrounded and if the rear outside wheel is less than or equal to noindication. The outputs of steps 370 and 372 are provided to an OR gate374. Thus, if either of the conditions in steps 370 and 372 are true,then it is determined whether or not the system is in a transitionmaneuver in step 376. A transition maneuver refers to when the system istransitioning or turning from left to right or right to left. If atransition maneuver is not present in step 376, the step 378 isexecuted. In step 378 the estimated lateral acceleration generated fromthe steering wheel angle is determined. If such an estimated lateralacceleration magnitude is less than a threshold, step 380 is executed inwhich the wheel departure angle is set to zero. Thus, the wheeldeparture angle should not be greater than zero when the system isabsolutely grounded.

Referring back to steps 370 and 372, the outputs of these steps are alsoprovided to an AND gate 382. If each of these conditions is true thenthe wheel departure angle is set to zero in step 380. After step 380,step 314 is executed from FIG. 12. In step 390 the front inside wheeland rear inside wheel are determined if they are absolutely lifted. Ifthese wheels are absolutely lifted the sum of the wheel departure angleand αθ_(xr) is subtracted from the reference bank angle. The α refers toa boost factor which, in this example, is 1.1. By subtracting thisnumber from the reference bank angle, the roll signal for control angleis increased. This is desirable in a system so that an absolutely liftedcondition increases the amount of control provided by the system. If thecondition in step 390 is not true, the step 394 is executed. In step 394if either the front inside wheel is absolutely lifted or the rear insidewheel is absolutely lifted, step 396 is executed in which the wheeldeparture angle alone is subtracted from the reference bank angle. Thus,this indicates that some increase and the roll signal for control isprovided. After step 396, step 314 from FIG. 12 is executed. In step 398if the front inside wheel is absolutely lifted and the rear inside wheelis not absolutely grounded or the rear inside wheel is absolutely liftedand the front inside wheel is not absolutely grounded, step 400 isexecuted. In this situation the wheel lift screening condition may stopchecking the wheel lifting condition. Therefore, the wheel departureangle is continued or initiated in this step to provide some hysteresisin the wheel lifting detection.

Thus as can be seen, the roll signal for control may be adjustedaccording to the wheel lift/wheel grounded conditions.

While particular embodiments of the invention have been shown anddescribed, numerous variations and alternate embodiments will occur tothose skilled in the art. Accordingly, it is intended that the inventionbe limited only in terms of the appended claims.

1. A method of controlling a vehicle having a plurality of wheelscomprising: determining at least one parameter selected from a linearcorner velocity, a rolling radius of a wheel, a rolling radius wheeldeparture angle, slip rate, and road torque; determining a heave normalload and a non-heave normal load; determining a total normal load as afunction of said heave normal load and said non-heave normal load;generating a wheel lift signal in response to said at least oneparameter and said total normal load; and controlling a safety system ofan automotive vehicle in response to a said wheel lift signal.
 2. Amethod as in claim 1 wherein a plurality of said parameters aredetermined, and generating said wheel lift signal in response to saidplurality of parameters.
 3. A method as in claim 1 comprising:determining a slip rate; generating said wheel lift signal in responseto said slip rate; and controlling a safety system in response to saidwheel lift signal.
 4. A method of controlling a vehicle having aplurality of wheels comprising; determining a wheel departure angle;determining an actual road torque; determining a wheel longitudinalslip; and determining a wheel lift status for said plurality of wheelsin response to said wheel departure angle, said actual road torque, andsaid wheel longitudinal slip.
 5. A method as recited in claim 4 furthercomprising: determining a relative roll angle; determining a rollingradius-based wheel departure angle; determining normal loading at eachwheel; and determining a wheel lift status for said plurality of wheelsin response to said relative roll angle, said rolling radius-based Wheeldeparture angle, and said normal loading at each wheel.
 6. A method asrecited in claim 5 wherein determining a relative roll angle comprises:measuring a roll rate; measuring a vehicle lateral acceleration; anddetermining the relative roll angle in response to a vehicle roll rateand the vehicle lateral acceleration.
 7. A method as recited in claim 6wherein determining a rolling radius-based wheel departure anglecomprises: measuring a wheel speed; determining a wheel linear velocity;and determining the rolling radius-based wheel departure angle inresponse to the wheel speed and the wheel linear velocity.
 8. A methodas recited In claim 5 wherein determining normal loading at each wheelcomprises determining a heave and non-heave load at each of theplurality of wheels.
 9. A method as recited in claim 4 whereindetermining a wheel departure angle comprises: measuring a roll rate;measuring a vehicle lateral acceleration; and determining the wheeldeparture angle in response to a vehicle roll rate and the vehiclelateral acceleration.
 10. A method as recited in claim 4 whereindetermining an actual road torque comprises determining a drivingtorque, determining a braking torque and determining a wheel rotationinertia.
 11. A method as recited in claim 4 wherein determining a wheellongitudinal slip comprises determining a slip power and a slip rate,and wherein determining a wheel lift status comprise determining a wheellift status for said plurality of wheels in response to said slip powerand said slip rate.
 12. A method as in claim 4 comprising: determining aheave normal load and a non-heave normal load; determining a totalnormal load as a function of said heave normal load and said non-heavenormal load; generating said wheel lift signal in response to said totalnormal load; and controlling a safety system of an automotive vehicle inresponse to said wheel lift signal.
 13. A method as in claim 12 whereinsaid heave normal load is a function of a vertical acceleration.
 14. Amethod as in claim 12 wherein said heave normal load is a function of aroll angle.
 15. A method as in claim 14 wherein said roll angle is arelative roll angle.
 16. A method as in claim 14 wherein said roll angleis a function of roll rate.
 17. A method as in claim 12 wherein saidheave normal load is a function of a vertical acceleration and arelative roll angle.
 18. A method as in claim 12 wherein the heavenormal load is a function of pitch angle.
 19. A method as in claim 18wherein said pitch angle is a relative pitch angle.
 20. A method as inclaim 18 wherein said pitch angle is a function of a pitch rate.
 21. Amethod as in claim 12 wherein said heave normal load is a function of avertical acceleration, relative roll angle and pitch angle and a vehiclemass.
 22. A method as in claim 12 wherein said non-heave normal load isa function of a vertical acceleration.
 23. A method as in claim 12wherein said non-heave normal load is a function of roll angle.
 24. Amethod as in claim 23 wherein said roll angle is a relative roll angle.25. A method as in claim 23 wherein said roll angle is a function ofroll rate.
 26. A method as in claim 12 wherein said non-heave normalload is a function of a vertical acceleration and relative roll angle.27. A method as in claim 12 wherein the non-heave normal load is afunction of pitch angle.
 28. A method as in claim 27 wherein said pitchangle is a relative pitch angle.
 29. A method as in claim 27 wherein thepitch angle is a function of a pitch rate.
 30. A method as in claim 12wherein said non-heave normal load is a function of a verticalacceleration, a relative roll angle, a pitch angle, and a spring rate ofvehicle mass.
 31. A method as in claim 4 further comprising: determininga pitch angle; determining a roll angle; determining a verticalacceleration; determining a normal loading due to a heave motion inresponse to said pitch angle, said roll angle, said verticalacceleration and a mass of the vehicle; determining a normal loading dueto non-heave motion in response to said pitch angle, said roll angle,said vertical acceleration and a spring rate of a suspension of thevehicle; determining a total normal load as a function of the normalloading due to the heave motion and a normal load due to non-heavemotion; generating said wheel lift signal in response to the totalnormal load; and controlling a safety system of an automotive vehicle inresponse to said wheel lift signal.
 32. A method as recited in claim 31wherein the roll angle is a relative roll angle.
 33. A method as recitedin claim 31 wherein the roll angle is a function of roll rate.
 34. Amethod as recited in claim 31 wherein the pitch angle is a relativepitch angle.
 35. A method as recited in claim 31 wherein the pitch angleis a function of a pitch rate.
 36. A method as recited in claim 4further comprising: generating a pitch rate signal; generating a rollrate signal; determining a roll angle from the roll rate signal and apitch angle from the pitch angle signal; determining normal loading dueto a heave motion in response to said pitch angle, said roll angle, avertical acceleration and a mass of the vehicle; determining a normalloading due to non-heave motion in response to said pitch angle, saidroll angle, a vertical acceleration and a spring rate of a suspension ofthe vehicle; determining a total normal load as a function of the normalloading due to said heave motion and a normal load due to said non-heavemotion; generating said wheel lift signal in response to the totalnormal load; and controlling a safety system in response to said wheellift signal.
 37. A method as recited in claim 36 wherein said roll angleis a relative roll angle.
 38. A method as recited in claim 36 whereinsaid pitch angle is a relative pitch angle.
 39. A method as recited inclaim 4 comprising: determining an actual road torque applied to thewheel; determining a calculated mad torque; and generating said wheellift signal in response to the calculated mad torque and the actual roadtorque.
 40. A method as recited in claim 39 wherein determining anactual mad torque comprises determining an actual road torque as afunction of wheel acceleration.
 41. A method as recited in claim 39wherein determining an actual road torque comprises determining anactual mad torque as a function of wheel acceleration and drivingtorque.
 42. A method as recited in claim 39 wherein determining anactual road torque comprises determining an actual mad torque as afunction of wheel acceleration and braking torque.
 43. A method asrecited in claim 39 wherein determining an actual road torque comprisesdetermining an actual mad torque as a function of wheel acceleration,driving torque and braking torque.
 44. A method as recited in claim 39wherein determining a calculated mad torque comprises determining acalculated road torque in response to normal loading.
 45. A method asrecited in claim 39 wherein determining a calculated mad torque inresponse to normal loading comprises determining a heave normal load anda non-heave normal load, and determining a total normal load as afunction of the heave normal load and non-heave normal load.
 46. Amethod as recited in claim 39 wherein determining a calculated roadtorque comprises determining a calculated road torque in response tonormal loading and longitudinal wheel slip.
 47. A method as in claim 4comprising: determining a braking torque; determining a driving torque;determining a wheel acceleration; determining an actual road torque as afunction of said wheel acceleration, said driving torque, and saidbraking torque; determining a total normal load; determining acalculated mad torque in response to said total normal load; comparingsaid actual mad torque and said calculated mad torque; when said actualroad torque is less than said calculated road torque, generating saidwheel lift signal; and controlling a safety device in response to saidwheel lift signal.
 48. A method as recited in claim 47 whereindetermining a total normal load comprises determining a heave normalload and a non-heave normal load, and determining a total normal load asa function of said heave normal load and said non-heave normal load. 49.A method as recited in claim 47 wherein determining a total normal loadas a function of said heave normal load and said non-heave normal loadcomprises determining a heave load in response to said pitch angle, saidroll angle, said vertical acceleration and a mass of the vehicle.
 50. Amethod as recited in claim 47 wherein determining a total normal load asa function of said heave normal load and said non-heave normal loadcomprises determining a non-heave load as a function of said pitchangle, said roll angle, said vertical acceleration and a spring rate ofa suspension.
 51. A method as recited in claim 47 wherein determining acalculated road torque comprises determining a calculated road torque inresponse to normal loading a longitudinal wheel slip.
 52. A method forcontrolling an automotive vehicle having a plurality of wheelscomprising: measuring a yaw rate; determining a lateral acceleration;determining a roll rate; determining longitudinal acceleration;generating said wheel lift signal as a function of said yaw rate, saidlateral acceleration, said roll rate and said longitudinal acceleration;and controlling a safety system in response to said wheel lift signal.53. A method as recited in claim 52 further comprising determining apitch acceleration and, wherein determining wheel lift comprisesdetermining wheel lift as a function of said yaw rate, said lateralacceleration, said roll rate, said longitudinal acceleration and saidpitch acceleration.
 54. A method as recited in claim 52 furthercomprising controlling said safety system to counteract wheel lift.